but the capitalist thing to do would be to put ads on both the paid and free versions of the service and infuriate all your customers to add penny shavings to your short-term bottom line!
No, the capitalist thing to do would be to optimize profit. Optimizing profit isn't some trivial thing, when there's competition (as there is now). It's literally optimizing the desire and will for people to pull money out of their wallet and give it to you. It's a chaotic system with many attractors.
If adding ads causes a reduction in profit, from people moving to add free LLM (there are many), then it would be capitalist, in the interest of profit, to not have ads. And, let's say there's a scenario where all the companies have ads, the capitalist thing to do might be to remove ads, to capture all the users that don't want them.
Sure, once competition is gone, capitalism stops working, but we're not even close when it comes to AI.