I doubt it's going to go the same way as search. You can't run Google on consumer hardware, but you can run LLMs locally.
At worse, newer models will get worse and you can just stick to older models.
You could also argue that proprietary models gated by an API are better than anything you can run locally, and yeah maybe those will get worse with time.
They're not going to get any worse than what you can run locally though. If they do, open models will overtake them, and then we'd be in a better position overall.