Why?

Why are they wrong, i.e. incorrect, unjust, dishonest, or immoral? And why must they be regulated?

The first point seems to stem from some unsupportable expectation of privacy on the public Internet. Get over it. If one is searching for and clicking around on sites for a new pair of shoes, expect to see ads for shoes.

This isn't incorrect. You've expressed an interest in shoes. How is it unjust, dishonest, or immoral to act on that? If someone observed similar behavior in a physical mall, would they be unjust, dishonest, or immoral for recommending a shoe store, even one they owned?

And why must advertising be regulated? Can't it just be ignored?

I'm targeted all day, every day. So what? I ignore most of what makes it past my ad-blocking software. Are we really so powerless, suggestion-prone, and thin-skinned that we need government to protect us from advertising? Good grief.

There's always going to be a profit motive. There are already laws like the CAN-SPAM Act in the U.S. and GDPR in Europe to regulate unwanted communication, data collection, etc.

But going even further, how is any of this "destroying the web"? I think you mean "funding the web".