So wouldn't it be fairer if, instead of this random seed, you use the current block hash?
No, the server seed has to be a secret, and different for every hand. If they used the same one twice, you could use the same client seed both times and get the same shuffle twice, meaning one you won a hand you could win it over and over again.
Please read again what I first proposed. Of course there needs to be a secret server seed. Bitzino has the initial card order as secret and then they add some random bits. Yet they cannot prove that these are actually random: I say that adding a public, changing nonce, and then doing the hashing, will make abuse very difficult, even once collisions are discovered.
The same system applies to gambling dice too, with a server secret and a pre-hash nonce.