As a Premier Silver I usually find a non-middle E+ seat at T-24, and keep looking for a better seat thereafter if necessary. I do check in as soon as the system will let me. I suspect the seats I get were often recently vacated by higher-level elites upgrading, if not showing on the seat map a day or two earlier.

To me, this is indeed the primary benefit of my status, so I do try to maximize it.

Of course, I don't travel that often, or I wouldn't be such a perpetual Silver.