"Progression-based power-gaming level-system", is the problem with most games that feature such things.
I hate such systems. Even in my old-school D&D games, which is where such mechanisms largely originated and where level (or hit die) is the prime gauge of power, I've always been eager to adopt and carefully enforce mechanisms that minimize the advantages level-based variables provide, whenever it's sensible (in my view) to do so. A 25th level fighter with 141 hit points can still be pulled to the ground and killed with a rusty spike through the eye slit in their helmet, in the span of two or three combat rounds, by a dozen sufficiently motivated kobolds (half-level creatures averaging 3hp each). That same fighter can also drown, have their throat cut in their sleep after a post-adventure debauch by a thieving prostitute, fall into a pit, or starve.
Anyway, I digress...the thing about level-based power is that it's supposed to be an abstraction of skill. One is not playing themselves, they are playing a character who has, over the course of their misadventures, presumably survived long enough to learn something that makes them that much more dangerous than those who are less experienced. This is abstracted into level and all those other stats that advance along side it.
Elite: Dangerous doesn't have and doesn't need this abstraction. It's a real-time, first-person, game where the CMDR you play has no statistics other than ranks, unlocks, and a bank/material balance...all of which have been rapidly depreciated as progression mechanisms shortly after their introduction. If you've played long enough to have any personal skill, you've play long enough to have had a fair shake at unlocking the relevant tools.
The arbitrary barriers to tool acquisition that are supposed to fill someone's desire for 'content' can be annoyances, but player skill (in a broad sense) is still the primary deciding factor in the final outcome of most competitive encounters. Most of those decrying imbalance because of a difference in character tools wouldn't do much better no matter what they had...they just lack the experience to realize this, which provides them with a convenient scapegoat for failure. You can (and probably should) take away that scapegoat, but it won't change the game's balance much.
I also disagree about a balance of power between combatants always being the desirable state of things. This is only the case if one is playing or simulating a sport. Plausible/organic combat should not resemble sport. It should vaguely resemble reality, where everyone involved is seeking to min-max the snot out of every aspect of every potentially hostile situation. Fair fights are anathema in anything resembling a real combat scenario...they only come about through strings of policy blunders and strategic failure. No one wants to fight their equals or betters if anything actually important (like one's life) is on the line. The goal is to stack the odds in one's favor as absolutely as possible, then hit the enemy when they are most disadvantaged. Of course things do not always work out according to plan, nor are situations frequently ideal, and there are countless ways to wind up with rough tactical parity in a conflict...which can be a hell of a lot of fun, at least as long as it's only one's game character's that have to deal with it.
To reduce every conflict into a well balanced sporting event removes much of the planning, roleplaying, and skill that goes into the doctrinal and strategic lead-up to those tactical encounters.
Regarding the part of balance where JHS states "you should start with roughly what your opponent has as well and victory should be decided based on who uses the resources they have the best", I completely agree. However, I'm not referring to the tactical scenarios, because tactics is a very small fraction of conflict. As it stands, every CMDR already starts with the nearly same stuff and same opportunities as any other. The only things I'd change in regard to balance here would be removing any sort of pre-order/backer advantages, removing all grandfathered equipment, and limiting the number of accounts and CMDRs per player to one.
Most organic PvP gameplay is not the few moments of tactical combat that occurs when one finds oneself within weapons range of hostile CMDRs...it's everything else. I don't want a system that ignores all of those gameplay opportunities just to make sure those who are willfully failing to plan, prepare, and anticipate can delude themselves into thinking they might have a fair shake at a tactical victory before experience proves them wrong.