No.

The purpose of "free speech" is to allow the spread of ideas.

The purpose of advertising is to spread an idea.

They are different things.

What?

Yes, the purpose of "free speech" is to allow the spread of ideas. The purpose of any particular piece of speech (a book, a pamphlet, a poster, a sign, a rally, a concert, anything) is to spread an idea. The idea in that particular piece of speech.

Do you want to preserve free speech but ban speech that tries to spread an idea? Your comment would be banned because you're trying to spread that idea.

Commercial speech is a legal term for speech that promotes commerce [1].

[1] https://www.law.cornell.edu/wex/commercial_speech

I mean, if you're going to make up your own First Amendment jurisprudence. But it would be worth reading the line of cases from Schneider through Sorrell (there's a lot of them) to get the reasoning of several generations of jurists on why it's not this simple.