I think everything revolves around the Power Budget. Everything else is pretty much a subset of that. Excepting Rewarding play/interaction which is, in my opinion, a separate design goal from balance itself.
Power budget is important to me. If the power budget it capped at some finite value (let's call it 100 units) and spent according to that budget, then everyone would be within that realm of "power." Naturally it means that if you spend some of those units on a strength, that creates a weakness. And that weakness leaves space for counterplay.
For example, if I spend 40 units on mobility, I'll have a very mobile character. Spend an additional 50 units on damage. Now I have mobile burst. Then spend 10 units on safety (so I have a conditional, limited safety skill). This is, naturally, an assassin. You'll note wave clear isn't on the list; safety is a very limited portion of that budget meaning their escape skills should also be fairly weak as opposed to a kiting champion. So i have very clear weaknesses: I can't wave clear so you can push me out and if I commit to a kill, I'm making a high risk play. Also, I'm fragile as all hell. Items permit me to either compensate for those weaknesses (Hydra, Guardian Angel, Randuin's) or bolster my strengths (Hydra, Black Cleaver, Last Whisper) but either way the character itself has a set of weaknesses and compensating for 1 thing means losing some strength in another section (excepting Hydra but I'm still melee at that point).
For a more concrete example,
gets 4 mobility skills, a shield, an AD steroid, an AoE execute, a pseudo-sheen, an AoE knock up, and a stun. All of this on low cooldown, resourceless skills. As one of the most mobile champions in the game, I'd say she should have like 50 units on mobility. An AD steroid gives her consistent damage as do her low cooldown resourceless skills. Another 40 units. 2 forms of crowd control leave her with another 30-40 units. Her pseudo-sheen and AoE Execute also give her burst. 30 units. Wave clear. 20 units. This is at least 170 units. It's ridiculous.
Contrast
. She's ranged so we'll say that's like... 10 units (because ranged characters have lower other things). She has a lot of CC (permanent slow, AoE slows, AoE slow + global stun). So we'll say that's like 50 units. Then, her passive gives her a minor burst and her E gives her the ability to farm additional gold and utility vision. Minor burst, 10 units. Vision utility, 20 units. Gold boost, 10 units (it's not very big, after all). At this point, she has 100 units. She fills a specific niche catering to her strengths (kiting) and does less damage than most AD Carries but can also initiate (globally) as a result.
A jack of all trades should have like... a 20/20/20/20/20 split and be very mediocre in most things. The problem is when characters have more of a 35/40/30/
0/20 split (probably so jack-of-all-trades feel rewarding). At this point, they become ridiculous and the specialists with a 50+ point investment in a single field are almost matched by a 40 point investment but these characters also have other massive investments.