Earlier quoted context omitted.
What's democratic about outlawing speech?
"Democracy is a system of government where the citizens exercise power by voting." https://en.wikipedia.org/wiki/Democracy If the citizens or elected representatives in a democracy voted to start censoring speech, but continued to empower citizens to vote, it would still be a democratic state in spite of the censorship. An illiberal one, but still democratic.
Only through the first election cycle [1].
Your idea is valid in a static, nothing-ever-changes world, with no significant political dynamics to speak of. However, out in the world as we know it, political processes run all the time, the proverbial pendulum swings, and consensus is formed via vocal advocacy and protests.
Right now we have four basic things defined as "political speech": person-to-person conversations; mass communication (press, TV, radio, online videos); peaceful physical actions like assembly and manifestations; and finally donations to candidates, parties and PACs. We protect each and every recognized form of "political speech" exactly because without it the important changes could not happen.
In a world with limited communication, you'd have on one side a small ruling clique, semi detached from daily concerns, a large mass of disenfranchised and zoned out people coasting along in the middle, and on the other side you'd have a small fraction of disenfranchised and either abused or outright persecuted people that can't even raise the wider society's awareness. This is an unstable state, leading to societal collapse in one way or another.
Let people speak effectively, lest they could not protest problems or oppression. Let people speak effectively, lest the wider society couldn't even learn of the problems faced by sub-groups. Being heard is the first, necessary step to having wants and grievances addressed.
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[1] tiptoeing around Godwin's law