If you saw the PPE you're supposed to wear for removing a cut out fuse you'd understand why, the issue is that the cut out can fail and arc.
I was really lucky enough to have witnessed a complete service head replacement by my local DNO only last year.
It was in my own home, from a fairly close distance of about two metres.
The service head and CU etc is mounted on the inside wall of my integral garage.
They removed the main cut out protection fuse first, then stripped out the old service head, then they working on the completely live side of the incoming underground cable to the service head.
The incoming supply was feed by a SWA cable, it had two large separate single core, aluminium conductors and a external CPC / Earth braided cable under the SWA protection.
It was a three man DNO team, one carrying out the service head replacement, who was wearing a LOT of the PPE equipment that you describe and then two others simply offering advice and watching every move he made, I think he was still in training TBH !.
It was very interesting to watch and the DNO guy's answered any questions that I asked them.
They where more interested in learning about my EV sitting on the drive really !.
For them it totally looked like a pure and simple "Gravy" job, but that is where the skills and training comes in I guess.
The whole job was completed ( plus a cup of tea thrown in ) in about 40 minutes, from start to finish.
My neighbour a few doors away, had his fuse upgraded by a sub contractor working for the DNO and they had the job done in less than 30 minutes.
They upgraded his meter tails and installed a 100 Amp DP isolation switch at the same time.
His EV installer was coming back to install his Zappi wall box the following week.
I believe it was the EV installer that contacted the DNO prior to his visit.
Similar situation with my next door neighbour, fuse upgrade first, then EV wall box installed at a latter date.
Mine was done the opposite way around, wall box fitted first, then fuse upgrade about two years latter, because I wanted to load shift more usage into my cheaper off peak rate !.
Our late night usage, would have been stretching the legs of our original 60 Amp fuse.
I feel much safer now that we are running on a 100 Amp cut out fuse TBH.
There was zero cost from the work from the DNO

.
The hardest part, was getting an appointment from them !.