Why does this USB-C to USB-A adapter have a chip in it?
Solution 1:
Based on the 3.1 power-supply mention, I'd say it's there as a PMIC to operate as a Power Delivery controller. Power Management IC (PMIC) can support DRD/OTG, Power Delivery, Vbus switching, etc. The adapters which have the chip bring additional cost, as you've mentioned, because they include PD & Configuration Channel functionality.
Solution 2:
You are confusing Type-C PLUG with Type-c RECEPTACLE. The pictured device has Type-A plug, and therefore goes into classic legacy Type-A receptacle, which is USB Host. The other end of the device is Type-C RECEPTACLE, which is supposed to be flip-agnostic. Therefore the receptacle should have intelligent means to detect plug polarity and multiplex the two USB-C line pairs into a single USB-A pair of SS lines. This function obviously requires a special chip, which likely combines CC-controller with a super-speed MUX.
There are primitive versions of Type-A to Type-C RECEPTACLE adapters, usually found as a supplement to USB flash drives. These are cheap versions, and work in SuperSpeed mode only when plugged with cable into one position. In opposite (flip) position of Type-C cable they work only in USB2 mode. That's why the price difference.
The USB-A to Type-C PLUG cables are indeed made out of passive wires, but fippability of the "legacy cable assembly" is provided by the TYPE-C host port, with similar electronics inside.
Of course, the above are just speculations. Without seeing the actual device photos it is diffucult to say.
Solution 3:
This adapter is junk and so are all others like it. The USB specifications explicitly disallow the USB-C/female to USB-A/male adapter shown.
The chip in the adapter may be there in an attempt to protect devices from damage that adapters like these like to inflict on both the host and peripheral devices. Since the function of these adapters is not defined by the USB specifications there is no knowing if it works, how it works, or if it will protect any devices from damage.
I realize that these adapters are quite popular, that people use them without damaging their hardware, but that does not change the fact that the function of these adapters were left undefined. There's no doubt many reasons why the function of these adapters were left undefined, and from reading many electronic specification documents in my life I have a good idea why these adapters were not allowed in the specification.
One good reason to not allow these adapter is that if a device has a captive USB-C cable then it is because a captive USB-A cable would have been insufficient to provide the power, data, or other feature that USB-C offers. If the device would work with USB-A then it would have USB-A, and people that needed to plug the device into a USB-C port would use the USB-C/male to USB-A/female adapter that was defined in the spec.
I know this is an old question but I'm seeing far too many questions like this and nobody is calling these out for the damage they can cause, often quite expensive damage. Using these kinds of adapters have been documented to start fires. Play stupid games, win stupid prizes. If this adapter is the solution to your problem then you are doing something very wrong.