Why don't RAID systems protect against motherboard crashes?
There are a few questions around here that make it clear there's no simple way to recover data from a RAID array after a motherboard crash.
The answer to this particular question suggests using an add-on PCI card (that can be moved with all disks to a new system without losing data). However, that just moves the problem (what if the PCI card gets fried?). Then there are NAS systems, but then again, what if the NAS motherboard gets fried?
[The "one and only" statement following this edit is incorrect, as Peregrino69 has pointed in his answer below.]
Keeping in mind that the one and only reason for RAID systems to exist at all is to preserve user data in the event of hardware failure (not counting RAID-0 here), I'd expect RAID technology to have solved this glaringly obvious problem long ago.
I find it plain ridiculous that, every time someone asks what to do with a RAID system and a fried motherboard, answers seem to go "hey, I once managed to recover from a similar situation using this one weird hackish trick - it might work for you". Also ridiculous is that data on a single non-backed-up SATA disk connected to the cheapest PC motherboard would be trivially recoverable after a motherboard crash, while data on an expensive RAID-5 NAS system would be mostly lost forever in the same situation.
Why isn't there a standard solution to this problem, designed at least 20 years ago, and implemented since then by all RAID systems worth the name?
the one and only reason for RAID systems to exist at all is to preserve user data in the event of hardware failure
RAID was developed to ensure of the availability of data in the event of a specific hardware failure, namely a disk failure. The in-question-excluded RAID 0 also can be used to extend a volume size over the capability of a single physical drive.
The data preservation tools are backup and long-term archiving.
As someone who has moved hardware RAID disks from a crashed server to a new server on several occasions, I disagree with the premise of the question. Software RAID has also been moved between systems. These have always been Linux servers, so I've never had to deal with situations where part of the RAID configuration is built into an operating system driver (somewhat common in Windows systems).
So, my question is: why isn't there a standard solution to this problem, designed at least 20 years ago, and implemented since then by all RAID systems worth the name?
The phrase you are looking for is "import foreign RAID configuration"
Not all RAID systems are the same in the way they work, many store metadata on the disks so the controller an rebuild the array configuration if it is reset or replaced (with the same model).. and there is a massive amount of variation between controllers and their supported features.
Imagine I have a RAID5 array with a 1MB stripe size across 12 disks on an Adaptec controller, and the controller fails, so I replace it with an Intel controller hoping to get my data.
Well it turns out the Intel controller does not support 12 disks in an array, only 8, and it has a max stripe size of only 256KB. Of course it is not going to work. Even if it did support those, the controller metadata on the disks is not even close in format to allow them to be read. And even if it did, does it use the same parity algorithm? The same stripe alignment?
As far as I know:
There is no standard on where to store array/controller metadata on array disks
There is no standard on what format to store array/controller metadata on array disks
There is no standard to even store array/controller metadata on array disks
There are many different ways to do RAID, the internal method may be proprietary
And why should there be a standard solution? The solution is simple, buy another controller of the same brand that supports import from the old controller model. There is not much incentive for competitors to reject their own methods or neuter their feature sets in the name of compatibility, when in reality the lack of compatibility is not a big problem.
Now, you had several examples that point out on-board RAID, there are two types here, consumer and professional. Consumer on-board has no interest in portability, unless it is the same chipset vendor, I have gotten Intel RAID5 from one motherboard to another, it reads the metadata from the disk and rebuilds the configuration. Professional on-board almost always expects that you will just replace the motherboard or server with an identical model, and once again it should just work. Many on-board pro grade controllers can also be purchased in addon card form factor, giving you another option.
As Peregrino69 answered, RAID is not backup, if you are trying to use RAID to protect against something other than disk failures, you are doing it wrong.
RAID is more useful at providing large increases in both logical volume size and performance when using multiple disks together, and doing it in a semi fault-tolerant manner.
"the one and only reason for RAID systems to exist at all is to preserve user data in the event of hardware failure" ...
No. In the context of all "RAID systems" that exist, this is the second or third most important reason, and should be used as a reason only when a lot of details the setup (what kind of failure it will protect from, what kind not) around it are understood. The assumption might be mostly correct, however, when it comes to Home/Small Business NAS boxen.
RAID is a technology that originates in the server world - where the reasons "provide continuity of operation until repair can safely and/or conveniently take place", "provide a performance benefit to read and/or write operations" (this is not limited to RAID0), "provide an easy to manage abstraction of the space provided by several disks" are at least as common and important as providing the limited backup capability you describe.
In the server world, systems (orders of magnitude more expensive) exist that use multiple relatively independent "motherboards", power supplies etc.
The recoverability of a RAID system if you lose the controller hardware, provided the drives did not get damaged or overwritten in the course, is really only a function of how the controller hardware handles this, what configuration data in addition to the disks it needs to recover etc etc. A raid controller/nas mainboard that leaves you with no easy recourse in that situation should be considered of faulty design.
However, a misbehaving or misconfigured (eg cache policies) controller can mean data gets actively overwritten or mixed with nonsense data. An electrical defect (eg a power supply that suddenly outputs too high a voltage, or a transceiver that shorts power into a data port) can result in physical damage to the drives. In such cases, recovery can become a non-trivial, non-automatic, incomplete or even impossible operation. A perfectly working RAID can perfectly consistently do data alterations or deletions caused by user error, malfunctioning software, or malicious software. These are some of the reasons why the reliability of RAID alone to provide backup is considered limited.
I can say with 100% certainty that you can replace a RAID controller card without loss of data, because I've done it on at least two occasions. The reason you can do this is that RAID controllers typically store the array configuration on the drives in addition to in their own memory, and the new card will just ask you if you want to import the configuration found on the drives. When doing this, you don't even necessarily need to have an identical replacement card, although that's certainly safest; a newer card from the same manufacturer will typically work as well. (eg, I recall that Dell supported moving an existing array from a PERC5/i to a PERC6/i, but not vice-versa.) The one thing to watch out for is that you need to make sure the drives are still in the same ports on the controller, or Bad Things happen. (On real server hardware with a proper backplane, the cables are often keyed so that you can't get them in the wrong order.)
However, I'd have far less faith in doing that with on-motherboard RAID. In my experience, built-in RAID tends to be terrible in many ways, and I wouldn't trust it with any configuration other than RAID 1 (and that only because you can just take one of the mirrored drives and use it as a single drive in another computer with no data loss; I still wouldn't try to actually move the mirror and trust the new motherboard to import the configuration correctly).
So, the answer is that there is a standard solution to the problem, and it is implemented on all RAID systems worth the name. It's just that motherboard RAID isn't worth the name.