The problem with checking this flop is that we're telegraphing a made hand, or at least one with showdown value.
For instance, we're probably checking this flop with hands like JJ/QQ, and sometimes with hands like AQ and AJ for pot control / to induce bluffs.
But when we check the flop, and then get aggressive on later streets, what hands are we representing? We would have c-bet the flop with total air-ball hands, like JT, and all of our small draws, like QJ and JT,
and all of our flush draws.
We wouldn't check the flop then get aggressive later with JJ or QQ, either.
So we're representing AJ+ on the turn/river.