But this will drive massive amounts of overworld gameplay by incentivizing them to go capture lots and lots of illuvials, because they are so useful to have large amounts of them. The marketplace would be much more active as there would be a better purpose for the low stats illuvials. This would raise floor prices across the board for Illuvials--at least compared to if this wasn't implemented and there was no purpose for a bunch of low stats illuvials just floating around on the marketplace forever. Stacking up until this generation of illuvials are finished.
Imagine you capture a Rhamphy that is 25/30 stats. Now you'll need to capture five more rhamphys to get to your perfect stats. That player would have just sold the 5 extra illuvials online instead. This will mean that lots and lots of players will actually just keep their extra illuvials to burn them to increase stats. More supply pinch. Sure, the whales will whale and just buy lots of illuvials for upgrades--but whales will whale in this game no matter what.
Yes, there will be a more perfect stat illuvials that exist in the world, but its value would likely be much more due to the supply crunch that this mechanic would put on the illuvials.
Lastly, we could add solan fuel costs to apply the Illuvial. This could be an excellent source of burning solan long term.