It's a good question, and frankly, doing so would save these studios a lot of trouble. So why don't they do it? Frankly, it's because of the money.
Anime studios need to take as many projects as they can to keep themselves afloat (an issue that studio Manglobe recently was bit in the butt for). Studios tend to work on at least one show per season, or at least as much as they can, if not even more than one per season. Why would an animation studio work on a show for next season, when they have the ability to work on a show for the season airing right now? They're constantly in a time crunch because they want to get to finishing up this current series so they can find another one to begin working on, and getting money for.
The other thing is that anime studios tend to work on contract, meaning that as they work, the money they get is already pre-determined by the anime's production companies (which are generally, but not always, separate from the animation studio). This means that anime production companies, from the start, need to pay the animation studio, even if the show hasn't aired yet.
The animation production companies usually don't get their money back until during or after the show airs (DVDs, Blu-Rays, merchandise, music CDs, etc.), meaning that until this money starts rolling in while the show airs, the production companies have a negative balance, as they've had to pay the animation studio, the voice actors, etc. So, for these companies, it makes more sense for them to have production start closer to when it airs, so they'll get their money back sooner.
There's most likely other reasons, but these are the biggest ones I can think of.