We're repeatedly told Starfleet are the best of the best.
Hmmm, when were we told this? I mean about Starfleet in general?
The Enterprise Dee being the flagship might account for why so many of her officers (high and low) are academy graduates. Look at the situation with Barkley, went he did not perform to expectations, Riker's first thought was to simply replace him, cherry pick someone else from within the fleet. How many first officers would be able to do that?
Did either Jadzia or Ezra Dax attend the academy? It could just be they didn't tell stories of that time in their lifes, or they received their commissions through another path.