I wonder if anyone has experimented with hydraulic drive systems?
Whilst it could be built, a hydraulic drive system compared to belt drive doesn’t offer many advantages;
Hydraulic drive - High torque, low speed, heavy, expensive, issues with heat build up
Belt drive - Low torque, high speed, lightweight, cheap, less issues with heat.
The above is relative to each other but that is why hydraulic drive is used in construction equipment and belt drive is used in motorbikes etc.
Following the motorbike theme, chain or shaft drive would be a more viable alternative to belt drive.