I know that what you've posted is just a sketch, but I don't think thinking of it as level adjustment is really viable.The default could look something like the below. 1-5 are how good the class is at the thing; c, e, i are the pillars.
Cleric: 4c, 3e, 4i
Fighter: 5c, 4e, 2i
Rogue: 3c, 3-5e, 3-5i (sum 11)
Wizard: all 1-5 (sum 11)
Think of the number as a level adjustment when comparing characters. A 3rd level rogue, 2nd level cleric and a 1st level fighter would be about as good in combat by default.
If a 3rd level rogue is no better than a 1st level fighter in combat, then when a 3rd level party with a rogue in it gets into combat, the rogue will be close to useless. Whereas when a 17th level party with a rogue in it gets into combat, the rogue will be fine if a little weak. At least as D&D has generally been structured, the effect of a level penalty is not uniform across the spectrum of levels.
This is what I would like to see.Each class should, by default, be at least competent in each pillar. No class should be, through any selection of options, be completely dominant in any pillar.
"As good in combat" is so vague as to be quite meaningless. A 4E fighter, rogue, cleric, and wizard are all competent in combat, but are they "as good" as each other? How do you measure that?
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I want each class to be able to contribute meaningfully in each, without having to sacrifice basic competence in the other pillars.
Some wiggle room is fine. If someone wants to focus their character on Exploration, and doesn't want to grow beyond their class's basic competence in Social or Combat situations, fine.
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I want rogues who are tricksters and scoundrels. I want fighters who are stalwart and strong. I want wizards who are masters of arcane lore. I want clerics who are wise and powerful. I want all of them to be all of these things in all three pillars.
I think this has to be very, very carefully handled.You are entitled to a small benefit in exchange for sacrificing access to one of the pillars
I will use Rolemaster as an example of a system which tackles this issue very conservatively. Depending on class, skills have varying costs. The default costing for a skill is X/Y, where X is the cost to buy one rank in the skill when one gains a level, and Y is the cost to buy a second rank in the skill when gaining a level. (Y is greater than or equal to X).
Fighters can get weaopn costs around 1/4 or 1/5, wheras thieves are around 3/6 or 3/7. And costs for climbing, stealth etc are roughly the inverse (ie 1/X for thieves, 3/X for fighters). This doesn't allow the fighter to get a better weapon skill than the thief (or vice versa for thieving skills), but it allows the fighter to get more weapon skills (in RM, each weapon category is a separate skill). A fighter is also far more likely to be able to afford to develop two ranks per level - but because RM works on a diminishing returns approach to skill ranks, this doesn't mean that the fighter's skill will be massively better than the thief's.
Anyway, this is a pretty structured and constrained system of skill acquisition. The ability of one class to pull ahead of another class in a skill, in virtue of the cheaper skill costs, is tightly constrained - by the double development cost, by the diminishing returns, and by the hard cap of 2 skill ranks maximum per level no matter how cheap the costs.
Nevertheless, by mid-levels hardly any RM thieves will be competitive in a fight when compared to an RM fighter, and at high levels the gap just grows wider. This isn't necessarily a problem as such, but it is a problem in a game in which each PC is expected to participate, to whatever extent and without actively holding back the party, in each pillar.
So I'm not sure that there should be any reward on the PC-build side at all for taking a flaw/disadvantage. Remove the incentives for hyperspecialisation. If there are to be mechanical rewards for flaws/disadvantages, I'd be looking at the action resolution side instead (eg if your disadvanatage comes into play, get a 4e-style action point - then when your time to shine comes around, you'll be able to contribute better without thereby mechancially overshadowing the other PCs).