That would be a world that I could live with. The only issue is mentioned above, the lack of viable minor league sports in america. The answer would probably have to be some sort of European style promotion/relegation system
You don't need to do pro/rel.
In the U.S. soccer ecosystem you've got MLS, the USL, and the NISA (if you want to add Canada in the mix, since MLS has three Canadian teams, you've also got the CPL). The USL has three tiers (Championship, League One, League Two with no pro/rel system yet -- might be coming).
Overall, there's maybe 80-100 professional teams of various levels in the country right now (I don't feel like counting them all up).
A lot of MLS teams have USL affiliates either in the Championship or League One tiers. For instance, D.C. United has Loudoun United as a USL affiliate in the Championship. Almost every MLS team also has an academy system beginning usually around U14 or U13.
So, the way player acquisitions work in MLS -- 1) you've got the homegrown contract (players who you sign directly out of your academy, even if they've been to college so long as you sign them before they declare for the draft), 2) if you have a USL affiliate you can also offer them a USL contract. 3) You've got your traditional purchasing player rights from other teams in other leagues. 4) trades within MLS. 5) Free Agency. 6) then several drafts (the Super Draft -- players who are coming out of college; the Supplemental Draft (basically the super draft rounds 3-6; and the player reentry draft (players out of contract or who have had their option years declined). It's a bit of complicated in MLS, but basically the Super Draft has become less and less of a big deal as teams develop out their academy system and use the USL affiliates to develop players.
One wrinkle, and it's something the NBA would probably have to do to keep parity, is an MLS team can put discovery rights claims on overseas players and if another club wants to sign that player they have to trade for their rights first. This way, foreign player acquisitions wouldn't go through the draft, they'd be negotiated directly with their club teams (which the NBA has to do on top of drafting them in the first place).