Don't think so - they're all very expensive because cell networks are expensive. You can get a burner phone, only use it as a tethered internet connection for your laptop which runs VPN software.
Phreeli seems to be the privacy promoting MVNO with the cheapest options. Not sure if it’s been audited or what its guarantees are, but anything is probably better than the big carriers.
If you cover your phone with an antielectrostatic bag it can't communicate; that is a Faraday cage.
Since people around you will think you are also wearing a tinfoil hard, you had better stick to the phones with hardware switches as sibling comment mentions
I get that anything emitting can be tracked and stuff. I'm looking to take a baby step where I'm at least not having every possible detail recorded and sold. That Phreeli recommendation from another user seems like exactly what I want (paired with other things like a VPN of course).