Direct phone-to-phone data transfer, on sound channel, is today inherently incompatible with the system. Some decades ago, an (even at the time) slow communication was possible by modems (with maximal transfer rate of 56 kb/s). Today the providers use various compression algorithms which optimize the sound transfer (for human voice), but limit the bit rate to about 800 bit/sec. Furthermore, doing it is inherently alien from the androids (although still possible).
What remains, that is the tcp pased, direct digital communication between phones.
Here the case is far more easy, if both phones are on the same local network. Namely:
- You can send and get files by bluetooth. It is similar to wifi, except that the practical range is only some meter. Bluetooth is a well integrated builtin functionality of all android phones.
- If the phones are on the same wifi network, you can install an sftp server on one of them (example), and then use an sftp client (example) to send/receive data. This is painful at first, but after everything is set up, it can be done nearly so easy like the "common" solution.
You can also have your own server (accessible over the internet, or accessible over a vpn) what you can use for a cloud-independent intermediate storage. This requires some skill to set up.
Direct phone-phone communication over the internet is problematic, but sometimes works. Typically ISPs dislike the incoming connections and they often filter them. Their reason is security, what could be an acceptable reason - if the whole behavior of the whole system would not point consequently to the direction, that somehow you always need to upload all your data to hostile USA companies (and "services"). If the ISPs you use do not filter so vehemently, you can do the sftp-based data transfer even if you are not on the same wifi.
You can also use your own home wifi router as a VPN access point. That means that anywhere on the world, you can connect home and enter virtually into your home network, accessing also the phones on it.
All of them requires work - "the system" very clearly does everything to prevent you from doing this, but it is still possible and you can do.
Another option is using tor to make your phones accessible from everywhere. You will need to learn, and in the reality, this is what prevents the commoners to doing that massively. A legal prohibition would not be so efficient.
Your exact system configuration, well that depend on a lot of things, but it is possible. All your options will require learning and work. Only direct data transfer over phone lines, over sound channels, is not possible.