"No speech should be illegal" - should I be able to threaten people then? That's speech. Should I be able to detail my plans for how I'm going to commit a crime? That's speech.
Should I be able to scream at the top of my lungs in a public space? Should I be able to use a loudspeaker to broadcast my voice (or an advertisement) to drown out all other sound in a public space?
It sounds nice what you're saying, but it's not what you actually believe, so I kindly ask you to argue less in bad faith.
My solution to the original problem would be to make it technologically unfeasible to solve. The architecture of the communication platform should be constrained in such a way that operators & owners are unable to make choices about which speech to include. This is because nobody is equipped to solve this problem, and nobody should be forced to do anything to try and solve it.