Was there? I don't really remember that. Most of the first 40 champions don't exactly fit that model.
I would think could be more impactful if those weaknesses were based around a kit instead of individual abilities.
I'm not seeing the connection between "there is generally a best skill to max first" and "weaknesses are based mainly around individual abilities instead of kits". There's a few steps you haven't stated there, and right now, I don't agree. As I see it, having skills that you can max first also means that there are skills that function fine without points, and that means I can use them together as an entire kit to fight someone. If every skill is worth maxing first, that means each skill has something that needs to be maxed, meaning that whichever abilities I choose not to max are just weaker, leading to more of a "1 ability vs 1 ability" playstyle than we have now.
This could be done if each ability had the same power budget.
Each ability having the exact same power budget isn't a great idea. First, it wouldn't accomplish what you want because there are some abilities which are always going to be more useful with one point than others. That's actually part of the reason why certain skills are maxed now. I don't need to max smokescreen on Graves because it does the job with only one point. I can't say that about Buckshot or Quickdraw, so they get maxed first. Same thing with things like Corki's Valkyrie. In order to make Valkyrie a viable max, I'd have to make the distance scale with levels or I'd have to shift a lot of damage to it, and neither would be fun.
I'm not convinced that this would add any choices or meaningful gameplay. You need to explain why exactly you think this will increase diversity, and maybe give some specific examples of how you would implement this.