The other exceptions are, literally, extremely limited to things which hold no legitimate public value like child pornography. If you can name only one legitimate instance of advertising then they are, by definition, proposing a content based prohibition of speech -- they don't like what these advertisers say while those other ones are fine because of whatever reasons.

They can change the laws but the courts place the burden on the government to prove that the problem can't be solved by any lesser means. And when they say "any" they really do mean "any", the problem can't be solved without making the targeted speech illegal.