Skin try out
Why not just make trying out a skin into a completely different system than the Hextech chests? I have Urfrider Corki and Aviator Irelia, and that's it. I play neither champ so I'm interested in neither skin.
So my thought is why not make it somewhat like TF2's weapon try out system. Maybe a few tweaks so that people can't unofficially perma-unlock a skin for free.
Remove the "Try out skin" in Hextech chests, and instead implement it in the shop. Every 7 days you get a skin rental token. At which point, you can choose any available skin in the shop to try out for a set amount of time. (Whether it be a few days, or just a few games)
Hell, why not make it so you have a chance to get skin tokens out of the Hextech chests? (As a bonus, not as a singular item you can obtain)
TL;DR Move skin rentals over to the shop, change it to a weekly token system, but for a shorter duration