That's the voting rights part. Freedom of speech gives you the right to tell your representatives how you want them to represent you. If you choose not to get involved in a contested issue, your representatives will think that the issue is not important to you. They will then prioritize their efforts accordingly. As far as everyone else is concerned, an opinion you don't act upon is indistinguishable from not having an opinion at all.
Freedom of speech makes representative politics a market, where effort is a key currency. You may dislike markets in general or think they are inappropriate in some situations, but they are an inevitable consequence of individual liberties.
What about a social media site for congressmen where you can only, like / vote / comment if you are a verified constituent and every post is linked to a real identity. And moderation was done wikipedia style. As in a comment may be removed, but you can see why it was removed and it's content and author can still be viewed via history or something similar.
This type of thing is only possible in an environment where there is roughly homogeneous values. When values diverge extremely on basic issues -- only 1 side will trust the tech owners not to shadow ban, astro turf, fake polls etc.
Bold of you to assume the congresscritters are interested in reading the letters written by constituents. At the local and state level I've had _some_ success in getting in touch with my local reps but when it comes to the federal level? Nothing. Every email I've ever sent is responded with the generic "Representative foobar is working for all americans blah blah blah..." followed by the generic press release they send out every few months.
It is the job of congress to write up and pass laws concerning matters I will never understand, and for which I am grateful that I am not obliged to understand.
Freedom of speech makes representative politics a market, where effort is a key currency. You may dislike markets in general or think they are inappropriate in some situations, but they are an inevitable consequence of individual liberties.