For image generation, this has already happened. To what degree, I can't tell, as I don't do image generation much so I don't have numbers on Midjourney subscriptions or any other image-AI-as-a-service sites. But civitai.com has become a place where people share their models, based off of Stable Diffusion or other similar bases, with various fine-tunings to achieve desired results. You name it, you can find a model for it at Civitai, and people doing some very creative things with them. (And also a lot of the obvious things, but it's the Internet, what did you expect?)
I haven't seen a text-based model sharing site spring up yet (perhaps they already have and I don't know about it yet). Civitai, being focused on image-generation, has the obvious advantage that it's easy to show off impressive results from the model on the front page of the website, and judging what someone's home-grown fine-tuned LLM will produce is a lot harder. But at some point I expect a Civitai equivalent site for text models, especially code-based ones, to become popular. That will seriously undercut Anthropic, OpenAI, et al, and will probably force them to find a price equilibrium.
Because once you're competing with "I spend $2,500 up front on a powerful video card, download an open-source model for free, and then I get pretty much everything I need for free" (additional power cost of running that video card isn't nothing, but probably not noticeable in your power bill compared to what you're already using)... then suddenly $200/month means your customers are thinking "after one year I would have been better off with the homegrown solution". The only way they'll continue to pay $200/month is if Claude/GPT/Gemini/whoever is truly head-and-shoulders above the "pay upfront once for hardware then use it for free afterwards" models available. And that's going to be doable, perhaps, but tough.