In the end, the company notices that when they make improvements to their algorithms, their revenue goes down. So they stop making improvements.
If it's pay-per-search there is zero friction for me to go to another provider.
It's probably not a practical charging mechanism, but it's an interesting thought. I also don't believe a monthly charging subscription is the right model but this is a tough one to get right.
There would be an optimum point where the results are good enough that people won't leave the service en masse, but bad enough that they spend way more than necessary on it. The optimum point is where the profits will be maximized for the search provider. Thanks to the advances is AI/ML/Data Science methods and tools, a savvy company will find this point and stays there until the point moves.
I first heard this idea from Richard Stallman many years ago.
I think at some point they changed the way it works and it fizzled out. I barely see it any more.
For YouTube: Maybe YouTube Premium is what you need then? No ads and you are supporting the creators you are watching.
Flattr also follows the subscription model. I want the busking model. I provide my payment details but not a penny is spent until I click the button for a specific video/channel/piece. The key is low friction. It can't be some third party thing where you need to click away. It needs to be right there where you choose what to watch/listen to.