Adding an elytra seems to defeat the purpose of hide and seek. You're meant to hide, not fly around. I think adding a temporary elytra as a power-up in a normal game of hide and seek could be cool, but just being able to fly whenever you want seems a bit iffy. I get that there'd be a cooldown, but it'd either be so short that it doesn't matter or so long that there's basically no point to having an elytra.
Some games lend themselves well to having an elytra. Games that focus heavily on killing don't seem to work in this way, at least in my opinion. Elytras allow for easy escapes and obnoxiously long chases. It's also stupid hard to hit someone while they're in flight. As a rule, I would just avoid using elytras in games with any sort of pvp fighting aspect. That's just my opinion though. Obviously some people enjoy pvp'ing with elytras (wings pvp, for example) but I'd be incredibly disappointed for an old favorite of mine to return warped in such a major way.