I think options will improve. The people that have what is needed to drive 240Hz at 4K is pretty low right now. I would expect in the coming years for that to change.
Let's just say, if someone does make a "smallish" 240Hz 4K monitor today, it's probably going to cost you.
Not really. The Samsung Neo G8 exists and went on sale for $1000 not too long ago. Not sure how much an "OLED tax" would add on but I don't think it would be too much more.