I've seen SMS spam maybe 3 or 4 times ever. Before Signal started permanently storing sensitive user data in the cloud (and refusing to update their privacy policy) I was using Signal for both secure communication and SMS/MMS and since I've moved away from them I still don't see any more spam now than I did then. I think the solution for the spam problem has a lot more to do with not giving your cell phone number out to every company who asks for it than it does what client you're using to read/store messages.

Of course the real solution should be on the network's end, but not giving out your number to any businesses is probably the best thing you can do while still accepting random texts from anybody.