Do people really write to their senators?

Politicians pay attention to what their constituents tell them in aggregate. Unless you've contributed a metric-butt-tonne to their reelection fund, they may not listen to you as an individual, but if you're one of a significant number of constituents for or against something, then they will often listen.

It is. I interned for a state senator and (I can tell you) that no complaints or personal feelings go directly to the senator.

Letters are also written by the interns. I could only imagine how much more extreme it would be for the regular senator!

it's surprisingly effective on small things, things they can fix by reaching into the government bureaucracy usually. Other than that, on big things, it seems to need an avalanche of mail to change them on a specific topic

I tried several times when I was kid and as an adult. No response, not even a canned response. I gave up on it. They are probably banking on that

It really seems that way