Young players require playing time to reach their full potential and get there a lot faster when they play more than 24 mpg. Historically almost every single hall of famer got significant playing time as a rookie. Even looking at the multiple time all stars, the same hold trues. Now maybe they just got playing time because they were good enough, that is likely part of it, but lets pose this hypothetical.
Boston drafts Fultz this summer. Fultz is either barely going to play because he is behind Thomas, Smart, and Bradley (and even Brown to a lesser extent) or he is going to take minutes from one of those players. If it is the former, then Fultz just isn't going to develop and might never reach his ceiling or might do so on a team other than Boston because it just takes so long. If it is the former, then what is the point in keeping all of those guys around if they are just going to lose minutes to a rookie? Might as well just open those minutes up fully and get something for the player that clearly won't be around long term anyway. Or maybe Zizic, how much is Zizic really going to grow playing 10-15 mpg backing up Horford for 3 years? Or maybe Zizic's ceiling really is Zeller so it doesn't matter.
There are certainly plenty of uncertainties, but you can't just try to rebuild and win at the same time forever, it just hamstrings both options because you either hang on to assets that could have turned into players that might actually win you a title or you stunt the development of guys you think could some day be a championship core such that they never reach their full potential. Couple that with some real salary decisions (I mean if you max Thomas, re-sign Bradley, Olynyk, Smart, etc. - how exactly are you going to re-sign Brown, Fultz, etc. - there just won't be enough money).
You based your entire post on a faulty premise that young players need starting minutes (after all, you said 24 mpg wasn't sufficient) to develop. They don't. They get the minutes as they earn them, not as they're given them. Look at the 2016 All-Stars. Jimmy Butler, Paul George, Kawhi Leonard, Lowry, Milsap, Green and so forth all didn't get more than 24 minutes their first year.
Some of those guys - like Lowry and Butler - really didn't play heavy minutes until their 3rd year.
The reason that most HoFers got 30+ minutes their first year is that historically most guys were drafted as juniors or seniors and their games were more well rounded. Of the Top 50 NBA players that were announced back in the mid-90s something like 40 of those guys were Seniors when drafted. Drafting freshmen rookies (and even guys who went from HS to the NBA) is a relatively new phenomenon. Garnett was the first HSer in over 20 years when he was drafted in 1995 and he's not even eligible for the HOF yet. So while your statement of "most HOFers got significant minutes their first year", most of those guys were 23 years old when drafted because that's the way the league was. It's changed since then.
So now that I've entirely debunked your faulty premise, let's address your remaining questions.
You're right that guys do need some playing time available to them as they earn it. That's an easy problem to deal with. You used Zizc as an example. If he's earned them the same way Jaylen Brown is earning his minutes, how about giving him the 20 minutes a game Amir Johnson is playing and move Al to PF where he'd rather play? What about giving him Zeller's 10? I'm sure Al wouldn't mind giving up a couple of minutes to conserve his aging body. That's 32 minutes without even trying much and Zizic isn't going to play 32 minutes next year.
Let's say we draft Fultz. If he's earned them, there are minutes to take from plenty of guys - IT, Smart, Bradley all play over 30 minutes a game. There are other minutes to juggle around. Finally, if they've earned them and there still aren't enough minutes to go around that's when you make a trade. Much like you make a trade when you need to extend Brown or any other rookie. That's an easy problem to deal with. If you want to extend Brown, you move Bradley. Most teams would kill to have too many good players competing for a limited number of minutes.
So say we did max IT and resigned Bradley - as long as the contract is still valuable there's plenty of cap space to go around in the new NBA. So if IT is making the max and Fultz is ready then you move IT. As long as you haven't overpaid for him, you're going to be able to get enough cap savings to sign your restricted FAs the following year. That's the GM's job.
Finally, high draft picks on good teams get the added advantage of playing against good players in practice day in and day out. When you get a guy like Garnett on the TWolves or Durant in OKC the only way for those guys to learn the NBA game is by playing because the guys their going against in practice are generally not very good. If you're a PG drafted by the 76ers next year, who the heck are you going to learn to play from on that team? Zizic, Brown and Fultz and the rest will be going up against good pros like Horford, Crowder and Bradley. They're getting much of their game experience in practice because of their level of competition.
Again I feel like I'm addressing a failure of imagination. These are EASY problems to deal with.
PS: We're not rebuilding. We're contending. When you win 50+ games in a year, that's not a rebuild anymore.
