What needs to happen is for mobile players to be on their own servers so they don't see the desktop players and vice versa. Since the two platforms are incompatible there is no reason for players on one platform to see those on the other one.
I understand the company's reluctance to invest the money and resources in setting all this up, but I think all users would benefit from this situation. The mobile experience is quite different from the desktop one (I have played both). I believe that if Top Golf focused on each platform separately, the mobile version would be free to expand and grow into something richer and more open that it is now.
The desktop platform would benefit too because the network would not have to handle all the mobile gaming traffic in addition to its own communications.