Kayle's new ult would fit Kindred better and vice versa.

I don't really see how.

Kayle > Divine enforcer of justice > Ult that bathes a target in golden light that temporarily protects them from harm before summoning a rain of swords to damage enemies around the initial target.

Kindred > Twin embodiments of death > Ult that temporarily prevents targets within a radius from dying and heals them afterwards

From a thematic standpoint it makes much more sense to give the battle angel character the ability to protect someone and then have swords rain down from the sky, and have the literal grim reaper character the ability to literally deny death in a "this isn't your time" sort of fashion.

... you want an ADC who likes to stay in the back and annihilate people to have an ultimate where you run up melee and can't auto attack?

Nahhh. Kindred's current ult fits them super well. Thematically with them being able to say when someone dies. Gameplaywise it may seem wonky at first but has awesome synergy with their kit and lets you pull some crazy teammate saves. It also synergizes with Kindred's E because you get them to the threshold, stack E 2 times on them, then throw the 3rd E right before the circle disappears and because it's an execute it will usually obliterate them.