And since the server provides both seeds, then the game is not provably fair because those seeds could be tested before the runs to warrant a looser seed for the long run.
To make it a provably fair game, users should be able to change the client seed before the bet.
So you're saying the server could get a seed designed to only give "heads" or "tails"? That's possible, but if the server tries to cheat that way, you can also use it at your advantage so that makes it a risky game to play.
They can do it for the first of few first flips but they can't keep doing it forever because of the
nonce which gets incremented after each flip.
The operator (server) can exploit this in their advantage if they can analyse the bettors gameplay.
Besides, why do they need to generate a
client seed in first place if the client can't customize it!