First of all, in all places I worked so far you could apply for "early promotion" if you felt like you were strong enough to qualify for higher rank before the official consideration time and some people were even encouraged to do so.
Second, it takes two things to be a good scientist: brilliance and persistence. If someone is in my field, I can usually estimate the former pretty accurately after looking at just one paper of his. However, to estimate the latter, I would need at least a 5 year record, which is pretty close to the standard "probation period" before promotion.
Third, the university administration, like any other management, wants to keep us on our toes for a while before loosening the reins. Whether that is beneficial or detrimental varies from case to case but one can hardly deny that it is more or less universally accepted management policy used almost everywhere from WalMart to NASA, so you'll need to put together quite a convincing argument to explain "why not in academia".
Fourth, even if one is a good scientist (according to the above definition), one still has to prove that he is a "good department citizen". In 5 years, you will actually face all "reasonable" situations and take most "normal" roles in the department except some extreme cases when one cannot predict anything about anybody anyway and establish stable (whether good, or bad) relationships with most other department members, so you'll become a "known evil" rather than "a cat in the sack" at the very least.
The only remaining question is "Why a cleverer person who is just hired has much lower salary than a less clever person who's been there 20 years?". In the European system, it is, indeed, almost always so but I should say that the US contract negotiating system is quite flexible here and I've been in the situation when the chairman recommended to several full professors on the hiring committee not to tell the (unusually high) salary that would be offered to a coming assistant professor not only to other department members but even to their colleagues on the committee itself with lower salaries to avoid unnecessary frictions, so the life is not so bad here as well.
These are the arguments "in favor" of the waiting period. I realize that there are ones against it too and can bring up a few myself but since the question was "Why is it there?" rather then "List all pros and contras", I'll hold the other half of my 2 cents in the pocket for now :).