All questions are in bold for ease of use.
The major carriers in the United States participate in NSA surveillance (except for T-Mobile apparently, because it's based outside of the US. Except they bought Sprint, which participates.) and that, along with other major privacy issues, means that the market for private carriers is incredibly slim. When I found out that some carriers, such as Mint Mobile, piggyback off of Verizon, I wondered: What's stopping a carrier from simply E2EE everything from Verizon, and then using Verizon to transfer the data? Obviously, the encrypted data could still be collected and sold, but it wouldn't matter if the encryption was setup properly, right? I'm looking to better understand how this works, and, if a solution exists, potentially be the first to make it happen. The reason I'm not suggesting creating a carrier without piggybacking is due to the sheer cost and lack of support it would have, which would lead to poor adoption. Also, if carriers simply don't support E2EE, couldn't carrier locked phones install the software (since most install software anyways) required to make E2EE work?
Calls are infeasible because you need to get a it of different parties on board, such as:
This requires a lot of coordinated work by a lot of people, and all the while the government will want backdoors for wiretaps and whatnot. It's just not going to happen. The technical problems aren't the great (if the signal is unencrypted, encrypt it; boom, legacy network support), so it's more that coordination that's an issue.
The next best option is a VoIP service that works with traditional phone numbers and encrypts everything between your device and the service. This wouldn't solve the broader problem, but encryption could be used by the service if the other end supports it. However, you'd need to only use VoIP on your phone, and the apps largely suck and there are technical issues like missing calls.
Text messages are being solved though with RCS now that Apple is on board and Google is marketing it, but unfortunately I don't think it's open enough for Linux phones to adopt, but I could be mistaken.