Recently I've been using Snowie to better understand flop cbetting ranges in single-raised pots in HU matches. I've run into a problem on the board AsTs7c. On this particular flop, the button is cbetting 45.8% of his PF opening range, including EVERY combination of 2-card flush draw.

My question is: what happens to Snowie's strategy on later streets if his flop checking range NEVER has a 2-card flush draw in it? 1/3rd of the time the flush card will hit, and if his opponent knows he can never have a flush, Snowie will be extremely vulnerable to overbets (basically, his opponent can make huge bets with any flush and most two pairs knowing he is very rarely beat).

Am I missing something? It seems highly exploitable to split your range in such a way that you can never have a nut hand on 1/3rd of river run outs.

Thanks for any input.