I'd be concerned about the life of the nozzles and the cost and availability of replacement parts.
The pump is one of the larger and more expensive components of the waterjet cutting system and also tends to fail at inconvenient times.
Our unis water jet crapped out right before we were to have final parts cut on it before sending them for competition. It was massive PITA
It's a good idea though.
A magnetic pinch would (I expect, I only really covered them a bit in a plasma physics course so I'm not an expert) basically pull all the suspended iron particles out of suspension and compress them into a thin rod, without actually compressing the water very much. My hunch based on semi-informed knowledge is that it just wouldn't do much to actually cut anything, but I could be wrong.
The other problem is that magnetic fields also produce a lot of heat in a conductor. The metal particles that clump up would probably sinter together or even melt. On top of that, it'd take a lot of power to run... pinches aren't super efficient.
Furthermore, since garnet has specific refractive properties different from other materials, could we pass all ferrous grains through an extremely high-speed discriminating chamber that looks for these properties in each grain, and magnetically directs the garnet grains back to the abrasive holding bin to vastly increase the recycling, while all other ferrous material goes a separate bin (for waste or other recycling purposes)?
I do love the idea of a Rail gun cutter, though - just not sure how it could really help cut things.
At normal fluid pressures -- the classic example being peeing on an electric fence -- it's hard to get much current flowing since there's so much empty space between droplets. But at thousands of PSI, is that still true?
The nozzle and hose are easy to exchange, and a replacement part with predictable wear is a plus from the manufacturers/investors perspective. I'd wager that the pump is the problematic part here.
Going a little off topic here: The failure mode you described reminded me of the horrible accidents that sometimes happen while maintaining high pressure oil systems in industrial machines. The smaller the hole, the worse the incident - human flesh and skin does not pair well with a thin, high pressure stream of fluid. I spare others the details, it's not pretty.
Do you think that a 'personal waterjet' poses more dangers to the operator than machines like a band saw or drill press?
With a waterjet like the one I use, you would generally have a computer moving the nozzle and not even have a reason to be near the nozzle. It also sounds like a jet taking off. I seem to remember the water speed being something like mach 3 exiting the nozzle, but don't trust my math on that. Cutting is done under water most of the time, which muffles most of the sound and splashback.
On the other hand, I carry a card that tells medical professionals how to treat me if I arrive with a waterjet injury. Waterjets don't work great on laminated materials, because when they hit a transition between materials, they tend to send their energy horizontally. This is also true if it goes through skin and hits bone. It basically shoots you up with water, air, and abrasive, which travels along or in your bones. I've never even come close to injuring myself with the nozzle, but it would absolutely be more scary than a bandsaw.
The closest I've come to injury was one day when I felt an eerie sensation of wind on my skin. I grabbed a piece of paper and tracked it down to a 1/4" stainless water line. I backed away and ten seconds later it was a white cone of fog from a leak that was visible for about 15 feet without even feeling wet. The moral of the story is don't feel around for leaks.
Amputation of extremities is not the worst case scenario :-/
Though they have less of a problem pumps pushing 7000-15,000 psi mentioned elsewhere on this thread instead of the 60,000 to 90,000 of traditional waterjet cutting machines.