I don't really understand why "provably fair" would be so big deal. The house is winning always, no matter what. But I don't gamble myself, so perhaps I don't uderstand that world that well.
Provably fair means you know exactly what you are dealing with before you start. Game payout odds are clearly displayed in the payout table.
1. The random number was generated before you even started. So the house could not change the number depending on the actual bets.
2. Distribution of random numbers over time. E.g. if the rule is "win when uniformly random number 0..1 is greater than 0.5", then you can check the history of all random numbers played (at least with your bets, if you don't trust the house to show real bets for other players) and calculate the properties of actual distribution. If it does not contain a significant offset, then it's fair. (Small deviations can be seen simply as part of the fee.)
The problem with your provably random method is that it is still possible for the house to get a slight edge. Since the server seed is random, you could regenerate it hundreds of thousands of times so that the house has a slight edge for the first two or three flips (assuming there are lots of people playing on the same deck, it gets wayyyy easier if it is one deck per person). You don't need that much of an edge to dominate your competition. An edge of 2 or 3% doubles your revenue; which would 4x or 6x your profit, since margins are usually thin for gambling sites.
This would make people believe you were paying out at a higher rate than you actually are.
I'm not suggesting you're doing that, just wondering what stops it, as I don't see anything immediately obvious.
the games are random and can be verified to be so. we publish the payout table. if you win we pay, if you lose, we don't.
other peoples historic results have no bearing on the authenticity of your game.