And you're leaving one crucial thing out: SCALING.
They scale their mana over the course of the game, with items that take time to scale to their actual stats. They can buy flat mana but even that isn't enough as their abilities consume large amounts of it. This is still their weakness since their abilities can consume their large mana pools if not properly controlled, but it's more or less not an immediate issue to overspend in longer battles.
What part of Kayle's kit isn't following the same paradigm? She scales into a permanently ranged champion, that actually hurts a lot in the late game. What Riot doesn't want to happen is that they intentionally create a champion's lane weakness whereas players just say "i'm just gonna go jungle instead". It defeats the purpose of the said weakness.
If she SCALES into the late game, she has to start with a weaker early game.
The big reason i think Kayle is considered weak is because her milestones are 6, 11, 16. These levels are nothing more than gates through which she attains her power as a champion, and often feel like plateaus until the next gate, than level by level scaling.
For the first 5 levels, Kayle has to work through worse early game than what she has had before (now melee). As soon as she hits 6, she can become range "on demand" IF she stacks per passive fully. So somewhat her old power level, that wasn't that great to begin with. The next 5 levels feel exactly the same when it comes to her trading as many champions get to their "ideal" stats and leveled abilities to be able to fight others.
Kayle on the other hand, still has to still until level 11 so that she gets this opportunity and praying that your opponent isn't ahead by a large margin for you to feel like you can contribute to teamfights or even win some 1v1s.
#TL:DR
I don't mind Kayle's scaling into the late game but i think that 6, 11, 16 milestones and large 5 level plateaus in between are the reason why Kayle feels weak. The power isn't evenly distributed in the first 10 levels, from 11+ is where her actual kit power spikes lie. Also keep in mind that Guinsoo's isn't her item anymore. Her waves aren't being duplicated by its passive.