Yeah, I do think there is a real issue with competitiveness if you assume the position that all teams should, factoring in GM competence, and luck as a thing that evens out, in a fair time-frame (like..20 years) have an equal ability to win a NBA championship.
And that's obviously not the case. There are outliers (San Antonio...pretty much just San Antonio, Dallas and Detroit, kind of), but by and large attractive markets win championships.
But I don't think that's a CBA thing, and its absolutely not a salary cap thing, that's a player movement thing. It all stems from players getting to choose where they want to play at critical junctures within their career.
And if they just want to severely constrict player movement (not saying that's a goal here), that would come with its whole other can of worms.
Without a cap, teams with the biggest pockets would take whomever they wanted until the salaries became unprofitable, or untenable. And the teams with the biggest pockets are usually in the best places to play. So double-trouble.