But to what extent will it be inaccurate? It seems unlikely to me that anything used for machining hard materials can be 100% rock-steady. Presumably, industrial machine are simply inaccurate to very small, tolerable degrees.

Accuracy and Precision would be problematic with this design, but, lack of rigidity is more insidious. Most of these high speed spindles will use carbide tooling, which is highly susceptible to breakdown under vibration. A flexible horrible frame like this is going to vibrate a lot even in materials like delrin or HDPE.

Also, with a vertical spindle and CNC control, there is no reason to have a vertical rotary axis. The reduced motion doesn't buy any capability upgrade. The 4th axis that is helpful would be angular. (you could put a horizontal spindle on this, I guess, but this machine is not up to the task.

Obviously there is no perfectly accurate machine for any application.

The extent it will be inaccurate depends on a lot of factors, such as tool length, material parameters, feeds/speeds, etc. You can probably cut aluminum somewhat accurately on this if you take extremely slow cuts, with a tiny tool spinning at an extremely high RPM (which keeps cutting forces to a minimum). Surface finish would still be pretty bad simply due to vibration of the arm. Likely going to break a lot of tools too. The majority of metal cutting setups you would do on a mill are simply impossible on this machine.

For a few tiny cuts, it might be handy to have one of these, but it definitely seems more useful as a 3D printer, plotter, etc. Though even most 3D printers are significantly more rigid than this design.

I have a small mill, it still weight around 1250kg… to be accurate at 0,01. And for that I would need to lock the unused axis and respect the power of the machine. This is not CNC, where the forces are often higher because they can work faster, with curve and some other things I’ll have a hard time doing.