I don’t see where the paradox lies.
When the right of free speech comes against other rights, e.g. right of life, property rights, then there should be limit to free speech. But not, IMO, against people who advocate intolerance invoking free speech. As long as they are not advocating violence, the answer need not be to silence that voice in the name of “intolerant towards intolerance”, but provide an equally but opposite voice. The right of free speech has already given us the tools to fight back intolerance.
So I am against the act of no-platforming. Let people advocating intolerance speak, but we shall answer them reasonably, logically, peacefully and as loud as they are, and in particular, reminding them the merits of tolerance (e.g. to prevent against the State of Nature/total chaos).
And I think we have to go back to the original argument for the right of free speech to see why free speech is important. John Stuart Mill’s On Liberty is my favourite.