Champion Design

I'd like to understand how the Riot team creates champions and decides which mechanics to give them. From what I've seen most Rioter say is that it's based around a thematic that a champion has in the conception phase of designing it, but what I want to know is when, if ever, does the thought of overbearing vs fun to play come to mind when making said champion. A few examples I would like to give are Nasus and Veigar, each champion has their own sort of stacking mechanic. Veigar's is for achieving an all-powerful state where your enemies should fear you, but he trades mobility for that power. Nasus on the other hand I'm a bit confused about, he too has a stacking mechanic but as far as i can tell he doesn't trade off much if anything for it. Kiting isn't an issue for him as he can just wither his opponents to a snails pace, you can't really kill him outright solo as he builds like a tank you NEED several teammates who do damage there to stop him otherwise he kills the carry then goes after the support because they can't do much to him.

Moving those examples aside, what constitutes certain champions gaining certain abilities and to a greater extent synergy with certain items in the game. What reason is there for abilities that clearly aren't auto's but treated as such to be synergistic with items that apply on-hit effects? What reason is there for abilities that apply a form of Hard CC to not be affect by Tenacity? What reason is there to gate some champions level powerspikes behind their ultimates while other have free access to them at the start of the game?

These are several question that come to mind when I try to imagine how a champion is conceptualized and balanced.