Can Continuation Betting be correct where players have no memory?

[Godfather80]

Okay, another semi-theory post from me based on the bizarre battlefields of NL25.

Basically, 90% of the players I play against do not follow players action from hand to hand. In other words, every hand is like the first hand for them. In this specific case, does it make any sense to continuation bet with hands? My conjecture is that, from a theory perspective, continuation betting only costs you money as it will rarely (if ever) force out a better hand, even if that hand is only bottom pair weak kicker. What are other low stakes 2p2ers thoughts on this?