Basebands fall under exactly which entities juristiction such that they can regulate a baseband to be 'entirely proprietary' ? I mean, BB + superhet. mixer => IF => carrier wave envelope containing your data. How do you even regulate a concept of physics? If you're paying the proper fees as a subscriber to $provider_foo you could even design your own receiver off the public standards documents.. (used to be a popular project for 4th year undergrads to do on FPGAs for the CE's who wanted to get closer to the silicon but MOSIS project space was reserved for only the EEs).
If you want a completely 'free' (as in GPL) cell phone experience, you can setup a OpenBTS transmitter and transmit at the 900mhz range which is commons property. To stay legal in the US, your antenna has to put out less than a watt, but the setup allows you to even use off-the-shelf phones and trunk into normal phone lines via standard POTS software. Your device would have to be something a-la http://alumni.media.mit.edu/~mellis/cellphone/ (just a janky setup, but just a proof-of-concept -- you can patch together components from DigiKey pretty easily these days; if you want free-silicon, I think the closest you're going to get is https://en.wikipedia.org/wiki/OsmocomBB or maybe some soft cores, but if you're actually going to take that soft core to tape-out, you're probably going to be running 6 figures just for masks...)
On the hardware side, there is a project "Free Calypso" to produce a completely libre (software, firmware, baseband, & hardware) "dumbphone" using the Calypso chipset.
Initially looking to reuse old phones with the Calypso chipsets, the project is now working on producing their own. Design files are completed; funding for the dev boards is about 66% complete.
If you want a completely 'free' (as in GPL) cell phone experience, you can setup a OpenBTS transmitter and transmit at the 900mhz range which is commons property. To stay legal in the US, your antenna has to put out less than a watt, but the setup allows you to even use off-the-shelf phones and trunk into normal phone lines via standard POTS software. Your device would have to be something a-la http://alumni.media.mit.edu/~mellis/cellphone/ (just a janky setup, but just a proof-of-concept -- you can patch together components from DigiKey pretty easily these days; if you want free-silicon, I think the closest you're going to get is https://en.wikipedia.org/wiki/OsmocomBB or maybe some soft cores, but if you're actually going to take that soft core to tape-out, you're probably going to be running 6 figures just for masks...)