Ah, the old, "If you have nothing to hide..." argument. Good for you!
Of course "someone" saves them (if you're not on Signal). That doesn't mean you ignore who all accesses them. Plus it's not just the texts you send, it's the texts you receive.
Something as heavily advertised as Signal and the fact it is free, calls me skeptical on if it really only encrypted between the sender and the receiver. Information is money these days, why do you think ads start popping up on things you texted or talked about on your phone? As one example.
Not causing paranoia but in regard to the nothing to hide jest, someone is always listening or watching, next time you go to town, just start looking around for all the cameras, these are the ones you can see, I'm pretty sure there are tons more you can't see. 30 years ago, all you needed was a pin hole in a wall for a camera to view out, I can't even fathom how far tech has become since then. I often wonder when I'm in the middle of a section of tall corn if I'm in a spot where no one is watching.