You're assuming way too much. It's been pointed out that just because they pick at these positions doesn't mean those players would be available at those positions. Trades, team needs, etc, would change every draft dramatically. Think about it. If a team is already good, and they get a top 6 pick, they don't need to pick the BPA. A good team can pick on need every time.
Basically, the middle teams greatly benefit from this, like the Jazz usually are. The bottom teams get hosed quite a bit. The top teams are the biggest winners. Big markets, for example, not only have a huge advantage in Free Agency, now you've given them top picks while they're great! That's less top picks for the bad teams.
In other words, let's say Cleveland still gets Lebron and then subsequently loses Lebron to Miami. How is Cleveland going to survive that if Lebron leaves outright with no sign-and-trade? Now Cleveland has to wait X amount of years before they can even get a chance at a top 3 pick. Let's face it, most years, there's usually a huge drop-off after the first 1-3 picks. It's rare when there's more than 5 All-Star caliber players. Therefore, without a trade or free agency, a team would be stuck in the middle of the pack for many years. They'd have to draft really well to make up for their loss.
Also, do you really think teams would trade away their picks as much as they do now? Teams trade away future picks with reckless abandon now because they don't think those picks will be any good because they think they'll be good. Do you really think the Nets would have given us so many picks if they knew exactly what they'd be? In other words, there'd be less of a chance of getting the better value out of a trade because the value, on both sides, would be much more quantifiable.
The Lakers, for example, wouldn't have had to trade so many picks to get Nash. The Nuggets and Magic recent trades, would've ended up less in favor of them, I would think. In other words, small-market teams would have less of a chance to recuperate their losses in free agency with a balanced draft. You're basically taking away an entire strategy, for building a team, away from the small markets that the big market teams don't use nearly as much. Why do you think the Lakers gave up so many draft picks? They don't need the draft like smaller market teams do.