Those who are wealthier pay more into the tax system, allow those who are less well off to gain access to things they normally wouldn't. This is a good thing.

Likewise, those who are wealthier are buying more products that are advertised, allowing those who are less well off to gain access to the internet for closer-to-free. This is also a good thing.

We can put limits on how advertising is done, give control over your data, etc etc. But the fundamentals stay the same.

So no: paying your way towards internet products won't save the average person money.

And what if there was a company (let's call it Google) that was extracting huge sums of money out of this social security/welfare system? Would this make you think that perhaps something was wrong about it? And that the system could be more efficient without this company?

At least for capitalism, the amount extracted by ad companies is known and taxed.

It's not fair to compare things in practice (captialism), and in theory (whatever you're suggesting).