I don't think this is actually true (eg. DPDK), but even if it is, you can put the driver in userspace (tun/tap + vfio/libusb/ioport/...) and still use TCP/IP in the kernel.
Speed certainly certainly isn't an issue for AX.25. The protocol typically runs at <10 kbps; the overhead of processing packets in userspace is negligible.
It most commonly runs at 1200bps, used for APRS these days.
You can do a neat trick with this if you set up IP over AX.25, particularly with softmodems. Since you've got IP you can do SSH or TLS over it, right? At least, if you set all the timeouts really long, because some of those packets take a while at 120 bytes per second.
So then you can tune the tones to be a little off the normal frequencies of one side, and play them through speakers with two PCs connected together. When you ssh from one to the other, you will hear the establishment packets and the flurry of packets for every keypress pingponging backwards and forwards between the two systems.
Absolutely brilliant for demonstrating how things like TCP works with retries (plug a mike into it too, shout some interference) and how UDP doesn't, and stuff.
And then you'd be able to hear the difference in the chat between the two machines! That's an amazing demo :-)
I used to use mosh and tmux over 9600bps AX.25 before I had 3G data, a very long time ago. Strictly speaking SSH over amateur radio breaks the rule about encryption but 144MHz is a big place with no-one in it, and you can't pay Ofcom to take an interest in what people do on amateur radio.