First of all, let's make costs clear. If power is extremely cheap for you (perhaps you make your own or have surplus from self-generated solar/wind), and you properly cool your GPU so that it does not burn itself out, then you MIGHT get a tiny amount of BTC from mining with a rig.
Nice Hash gives you about $1.78 per day for renting out an Nvidia 1080 Ti, so you would get $1.78 per day if your electricity costs are zero. A 1080 Ti is about $1125 and uses 250W. (2190 kWh per year, if ran 24h/day). IF you have free electricity, and given that the Bitcoin difficulty does not go up, this means you get about a 57% yearly RoI, and from this you must pay the 22MWh of electricity.
Now that the return rate is clear, the vast majority of GPU miners use a GPGPU language such as CUDA or OpenCL. You do not need 3D acceleration, "only" GPGPU.
But GPGPUs allow accelerating more general computation than 3D, so chances are it's a more difficult challenge to implement as free software. If you don't have drivers for 3D acceleration, it's even harder to have GPGPU drivers.
Here is the Nouveau feature matrix for reverse-engineered nVidia drivers. Note the "WIP" in the last row - the "Compute" one. That is GPGPU support.
I share your frustration, I wish to sometime use GPUs as neural network accelerators, but I refuse to use nVidia's proprietary drivers which offer me little control. I could not even get the temperature of the GPU from the proprietary driver, let alone throttle the card to prevent it from melting itself.
