Some ostensible reasons:
- The flour absorbs the surface moisture and the meat browns better -- or at least differently.
- Loose flour is incorporated into the broth/sauce/gravy and browned flour tastes better. So, two birds -- flour and meat -- with one stone.
- The flour alters the surface texture of the meat -- something like "velvetizing" in asian cooking.
- The flour absorbs the surface moisture and the meat browns better -- or at least differently.
- The browned flour is already flavored with the meat's essence, when the meat is removed and the aromatics browned.
- More and better (mo bettah) fond for a better deglaze, when the meat is returned to the pan and liquid added.
There are other reasons, but they aren't leaping immediately to mind.
BUT
When it gets down to it, it's more a matter of style than anything else. You can do a perfectly fine job of stewing and braising without dredging before browning; and I certainly wouldn't call not dredging bad technique. To the extent that excess flour will be used for thickening, the un-dredged meat may be removed and a little flour added to the browning fat either before or with the aromatics (or, if using, before or with the tomato paste). Of course, sauces may be thickened after the rest of the dish is cooked with flour, other starches, or simply by reduction.
The modern trend in high-end, "International" cuisine is to use as little flour as possible -- and that's had a lot of influence in "New American Cuisine" as well -- even reaching into contemporary interpretations of "Pennsylvania Dutch" and Southern styles. Based on what I've read, the dredging is less common than it used to be among professional cooks at the high-end level.
That said, my own approach (to comfort foods especially) is "old-school" and I often dredge before browning -- especially when the ultimate sauce or gravy is meant to be opaque.
It just depends,
BDL