It would certainly be possible to make a machine like you are proposing, but there are good reasons why hydraulics aren't usually the optimal choice. There are exceptions to this, for example CNC press brakes for metals or CNC mandrel benders often have hydraulic actuators. The distinction is that usually the down sides of hydraulic positioning are only worth it if you need a lot of force to complete the operation. In your case with a hobby-scale CNC mill all of your travel axes can operate on very little force.
Here are some of the down sides to designing for hydraulic actuation:
- Speed: even smallish hydraulic cylinders require a significant volume of oil, and there are practical limits on the flow speed inside of hoses, so moving enough oil to get a hydraulic cylinder moving as fast as a lead screw or rack and pinion can move would require a large pump, large hoses, and large ports. All of this is possible, but very expensive as compared to a simple stepper or servo motor.
- Leakage: By there nature, pretty much all hydraulic valves involve some amount of leakage. Part of designing hydraulic systems is characterizing the amount of leakage and taking measures to compensate for it where the consequences are unacceptable. Again, it is possible to overcome these challenges, but buying high-precision valves, detailing counterbalance circuits, and maintaining the seals are all unnecessary costs.
- Controls: Hydraulic valves have moving parts that take time and power to actuate. They don't have perfectly linear responses with respect to time, voltage, or pressure differentials. As a result, achieving precise position control requires more careful control tuning and feedback. By contrast, for a hobbyist level machine using stepper motors, you can pretty much treat this entire challenge as a solved problem. Even at a higher level, configuring a VFD and controlling its setpoints is much easier than controlling a hydraulic valve with feedback.
- Cost: Aside from the ancillary challenges of integrating hydraulic actuators into machine design, the actuators themselves are simply more expensive. Hydraulic components are not produced in the same volumes that electric motors are, so there's not nearly as much of an economy of scale. In general hydraulic parts require more precise machining, more raw materials, and more detailed QC than motors, all of which translates into cost.
- Routing: Whereas an electric motor can be driven by one cable with power and control, hydraulic actuators need two hoses at a minimum for precise control in two directions. The hoses are much larger and stiffer than corresponding cables, and failures are more of a mess. When an actuator is being moved by another axis, the logistics of routing the hoses is a fairly big pain.
- Serviceability: Most users are better equipped to service electrical equipment than hydraulic equipment. A simple multimeter can allow a wide range of diagnostics on electrical equipment, whereas one needs a fair number of gauges and fittings to really find a problem in a hydraulic circuit. Even more than that, hydraulics are harder to disassemble since pretty much everything is a pressure component and can create a big mess.
