If it's easy for one player to get a flush or straight, it's also easy for
the opponent to do so, and it evens out.
In my predesigned deals, players start with 2 pairs, and making a flush
requires you to lose 2 hands. In a random deal, both players might start
with a flush, which would cause near-paralysis of the major piees, or both
players might start with weak hands, allowing a flush rush. In either
case, what's the problem?
The card you get from the Pawns is somewhat like a wild card, which of
course makes flushes and straights easier to get.
Segregating the suits was done to ensure fairness, but of course that does
make flushes more likely. The alternative would be a fully random deal,
unequal cards, but either player can reject the deal before the game
starts.
I see we already have two variants of Poker Chess. I am surprised that
neither is based on Night Baseball.