What good are Divers?

In Disgaea 5, there are items called Divers that can be found in the item world, that immediately advance your progress through the Item World by a certain number of levels.

In previous Disgaea games, these would have been a huge boost, but in Disgaea 5, your item only gains an item level if you play through the level and defeat every enemy. Skipping over stages with Divers, then, appears to not have any beneficial effect on your item.

What's the purpose of having them?

It's been quite a while since I've played, but I remember that near the end of the post-game grind, powering up items focuses more on defeating the Item Gods than actually clearing the floors in the Item World. Defeating Item Gods provides much more useful bonuses than simply leveling items up, and the grind to defeat Item Gods will very quickly surpass the grind to hit max level on an item. The Diver items allow you to skip straight to the boss floors to expedite the grind.

There are some more thorough explanations online in threads like this one:

Saves time getting down to the IG2 in R39 items. I usually have the item up to L80 as is necessary to spawn the R40 equipped God by floor 55 or so. You can just skip the rest to floor 100 after that.

After maxing the stats on the item themselves you may still want to go through further and get unique innocents in the item. You get one per God killed, so it'll help with skipping down to those as well.

The main use is in power leveling item. To make a perfect item you need to do 4 things. First get the level up to 500. Second get the Kill Bonus up to 400 (if you do item world a 20 stars it goes faster). Once you get these done increasing them doesn't make the item any stronger. Now the next two parts are where they come in to play. Third get the Training Bonus to max out. Once you get the first two out of the way the fastest way to max out the training bonus is to fight the bosses on every 10th floor. Using the Female ninja's evilaity and the adventure squad (turn on boss floor forever in the cheat shop) you can skip 5 floors and fight a boss every other floor. Finally the Item gods give you a innocent when you beat them and there are 48 in total. Using Diver-10s to speed this up cuts it down to about 3-4 hours assuming you have enough.

Or this one:

You must kill 46 item gods just to get each unique innocent. That is 4600 floors. Reaching floor 10000 grants a 100% dupe rate at dupe rooms, and is generally something you want to do with at least your Trap, since you will need 3 of them for every character you plan on using.

If you want to do that floor by floor, then be my guest. You will cap out the Item level long before you reach these depths, and be wasting dozens, if not hundreds of hours needlessly clearing floors. The rest of everyone will be skipping 20 floors at a time.

Additionally, killing massive amounts of Item Generals, Kings, and Gods without leveling the item is the only way to pull an Axe out of negative Hit and Speed.

Divers aren't for general use. They have a very specific use, and are unmatched in that use.

Long story short, when you're doing the seemingly unending post-game grind, Diver items greatly expedite the process without any drawbacks.