His platform is not that speech needs to be reduced. It's that as many parties as possible need to be able to have a voice, and because certain entities can spend dramatically more money than the rest of society, they can drown out the voices of others.
It does reduce the ability for people to speak. You said it yourself, it makes it so they can't drown out the voices of others.
People are not equal and we need to recognize that; some are famous - their speech is hear by more people than mine, some are rich, some are well connected, some are beautiful, some own a newspaper, etc. Not everyone has the same voice, and that's ok.
Lessig gives specific examples of possible policies to illustrate that it's actually an increase in speech rather than a decrease in it, here: https://mayday.us/the-plan/#fundamental-reform-in-the-way-el...