The Wheel as a strategy doesn't scale well, though. A good stock for the wheel has relatively low volatility, but with high volume of option interest. These two things are kind of opposed to each other, though. If a stock isn't very volatile, then there isn't much need for large option interest.
Of course there is a lot of overlap where things get interesting.
I think the reason why there aren't a lot of institutions running the wheel et. large. is because it just can't work at the scale they want to operate on. You can probably run the wheel pretty successfully at a million in capital (much larger than I'm used to), but at 10, 100, or 1 billion, it just doesn't work.
And what are they going to do? Pay some guy 200K to generate maybe 200K on a million in capital?
Of course, you might have better luck wheeling on something with much more implied risk than SPY or cycling through some of the most risky stocks. But depending on where you are in the wheel, you are still yourself assuming risk that can make you lose money (e.g. a collapse in implied risk while you hold the stock).
When you say wheeling works best on a stock with low volatility and high OI, what you mean is that it works best on a security with under-priced risk. I am sure there are actually many funds running strategies based on exploiting over-priced risk premiums. They just have no need to trade options on the open market since they can work with a market maker who can take the other side for them.
The financial industry would not just leave that much risk-adjusted return on the table, after all. Just because a strategy is complex does not mean it is lucrative.