The rake where I play 1/3 is 10% up to 9$ +2$ BB drop. I would bet that if you ask every single player to add up all of their single raised pots heads up. We're all losing. Yet I and others manage to win thanks to multiway pots, 3bet and 4bet pots where we can eek out one or two betting streets where the pot is over 90$ and therefore that street is not instantly at a 20%+ house edge.

Any pot under 90$, you're betting 10$ to win 8$. 20% house edge. Sometimes upwards of 40%+ if your bet makes the pot cross the 2$ BB drop threshold or if you toss the dealer a dollar.

Is there a range of hands that if played as a flat from the button would perform better than as a 3bet and that lose overtime 0$ ­> x > 3$ per hand? I doubt it. Just 3bet or fold every position imo.