I've always wished that Cover let you do something similar to traditional Final Fantasy games, by letting you gap close to an ally.

I think the idea of changing to Cover to a permanent uptime buff like Dance Partner is interesting, because that's functionally how Knight's Code/True Knight worked. Perhaps while it's active, your chosen teammate also has a chance to block incoming attacks, with the rate augmented if you use Bulwark. And then perhaps you can use Intervene to gap close to your chosen teammate for some sort of a combined defensive buff (you'd have to take the damage off Intervene if you do this and make it into a pure mobility tool, but I think that's a better design choice for gap closers in general). The cooldown could be for re-applying it to a different target.