I'd be in favor of significantly taxing advertising for the same reason that we levy "vice taxes" on booze, cigarettes, gambling, etc.
It would at the very least reduce the amount of it and select for advertising of a higher quality, cutting the noise a little.
Taxation shouldn't be used to curb habits, that's what laws are for.
Well, we have to balance that with advertising funding a ton of things that we otherwise value but would rather not pay for. Transit, free wifi, little leagues, etc.
I worry that such a tax would create a self-reinforcing monopolistic effect by making it harder for smaller companies to do it, thus enriching those that can afford to do it. Even if there's a threshold under which it's not taxed, it still benefits big corporations.