There's an app, Silence[1], which encrypts your SMS if your contact uses it as well. It does so over the actual telecom SMS network, and doesn't break non-Silence user messaging either. Been using it for years.
There once was an app called TextSecure, who pioneered E2EE on phones, that used to work both with SMS and its own network. When they realized maintaining both networks was hard, they ditch SMS and remained on their own network. Some unhappy devs wanted to keep SMS compatibility so they forked the app, focused on that, removed the custom network named their fork SMSSecure and, after some time, called it Silence. The original devs used the opportunity of a groundbreaking change to rename their app... Signal.
You are absolutely right. I started out with TextSecure myself. I switched over to what became Silence eventually.
I'm not a Signal user though after giving them several tries, and that decision seems more final by each passing days. I find I disagree too much with how their leadership and organization have behaved in relation to other projects and the direction they continue to take Signal.