So why not go one step further and burn a few books? Your "no platform" approach is merely likely to encourage already existing disdain that many ordinary people have for the way the left operates. Commonsense says that if you're not even prepared to allow these people to air their ideas and then confront and defeat them, there must be something fishy about you too. Most people are, understandably, likely to feel insulted by a paternalistic approach which says they're too delicate, immature or reactionary to be exposed to a few backward arguments.
On top of this, left censorship merely feeds into current establishment suppression of political debate which these days is usually premised upon the need to suppress racist/sexist/violent/abusive ideas - but of course generally ends up silencing anything a bit too radical.
Russell