Non-specialized characters could still be made, they just wouldn't be as effective in the later stages as a specialist would due to not being particularly good at anything. Would be an interesting challenge though.
Mutually exclusive perks are a staple of the 'tree' system, since specializing in one direction often locks out another due to conflicting requirements.
It like this (in my opinion): When you spread the bonuses to 29 picks, they are bound to lack in substance, otherwise you will be a god. Going with this, picking 1 perk doesn't mean much at all and to reap any reward the perks are supposed to offer, you need multiple of them. The gradually growing, is primarily the job of the skills, which the perks are then supposed to enhance. But since the perks lack in substance on their own, the enhancement is felt much, much later.
Now, if you squeeze the 29 to 15, the gradual progress is much more visible and (I'd think) more satisfying to the player since the waiting for the stack to grow high enough to present the progress that is intended is compensated somehow. And all this would likely happen with same effort and time, and resulting in same situation as with more picks and less substance, but with more satisfying progress.
Specialists would still prevail, but even non-specialists would get something more out of it though having some harder times. It's not really "Hey, look! I got a cool new perk!" but more like "Hey, I think this'll come in handy". And, I must stress, I'm not wishing the perks to be overpowered by any stretch of the word.
And lastly, it's just my personal preference to not be constantly rewarded with "bonuses" (and I'm admittedly a traditionalist in this regard), and it (imo) would keep the perks more interesting throughout the game.
All in all, though, this is all dependant on what the perks actually do, more or less perks given.
(how much am I repeating myself? B) )