No, people would still go for the free product, killing the other option.
If Google charges $1 per month for no tracking whatsoever, I'd bet that the vast, vast majority of the population wouldn't pay.
"No tracking" only, not "no ads". No ads would be far more expensive.
But you can actually do it: buy a corporate account from them and then use an ad blocker. As simple as that.
Now go and put your money where your mouth is :)
That's not how companies price services. Not by very, very, very far.
There are many pricing strategies designed to make heavy users pay more and light users pay less, or rich users pay more and poor users pay less.
Ideally, a company would charge a different price from every single user, and that price would be max(100% of the willingness to pay for that user, marginal cost of that user).
That's usually my mindset.
I mostly see companies as very rational actors, and assume that different options usually have been looked into and discarded in a rational way. Therefore, whenever a company is doing something that doesn't make sense from my POV, I usually think (unless there's clear evidence against it) that there are solid reasons for that.
Sadly, most people (here on HN included) seem to act in a "I'm really smart, and if others are not doing what I think they should be doing is only because they are stupid, not because I don't have the full context from my armchair".
It's one of the aspects of game theory that I like the most: you have to force yourself to consider other agents rational and intelligent actors who will (in the context or corporations) chase profits just as you would.
That's why I trust companies far more than people or the government: I can always trust them to chase profits.