You are absolutely right, and to add, I personally have not come across any casino that listed a token that belongs to another casino on the platform, I believe it's safe to say that this is due to the heavy competition among online casinos, every one of them is trying their possible best to become the best, and I believe they probably see listing a token belonging to another casino as helping such a casino to climb up, which is something they don't want to do, this is just pure business ethics I believe.
Apart from the competition so far there has been no casino token that has impressed its performance so that it can attract many people to invest in it, even some casino tokens that can be said to be famous have trading volumes that are also very small compared to the coins that many casinos use as their means of payment, so if some casino put it in maybe not many will play with the token because there is a fear that it will be difficult to sell it because of the low trading volume.