I had three phase fitted many years ago by the then Norweb local supplier. It is a long story but I was fortunate to have it done for free. One problem that I have found is that since the de-nationalisation of the supply industry it can be quite difficult to find a supplier who will support a three phase supply to a domestic property. Most of them now require meter readings via a website or app. However they only have a system for a single reading on the afore mentioned sites.
This leads to difficulties especially when contacting them over the phone. When you mention three meters they think your property is divided up into flats or that you have an ordinary meter, an off-peak meter, and can't count properly. Other problems can arise if one meter has a lower reading than the other ( normal on a mixed three phase / single phase supply) they then think you are doing something dodgy. It means for me that I am tied to one company who do seem to be able to cope. It also helps that I can work quite happily on three phase and fit my own wiring etc.
I have never had a problem running the domestic system alongside my three phase. Everything was done to sixteenth edition regs. originally and seventeenth edition later (not much difference in three phase) The main advantage of the three phase is the loading on a higher voltage is less than by using a VFC on a lower one. And it does depend on the number and types of machines you want to run. Some of my machines especially the specialist swiss types would be extremely difficult to convert or run on a VFC because of the integral multi pole motors used. Although I have fitted a three phase 415v Input inverter onto one of them for the speed control.