This is about quenching, which happens in emergencies or failure. During regular use helium is recycled in similar systems often today. But it's simply not feasible to do that when all the liquid helium in there evaporates at once
This only happens in an emergency, not during normal operation.
Pretty much the only time you would do it when a person is stuck in the machine by some piece of metal that is attracted to the magnet. You hit the quench button which vents all the helium, but more importantly also halts the magnet (all the energy released from halting the magnet goes into boiling the helium), and then you can release the person.
You don't do this for any other purpose, for example if some metal cart is stuck in the machine, but no one is at risk, you use a slower method to shut down the magnet (i.e. drain the energy) that doesn't vent the Helium.
I was under the impression that metal 'sticks' to an MRI machine with so much force it will usually puncture the machine and all the helium will leak out ..
The issue in that respect is that they flood the coils in a helium bath, instead of utilizing additional structures like channels/nozzles to provide the same rate of freshly cooled helium to the heat sources as the bath does, but with far less helium required in the system.
I don't think any similar magnet exists that doesn't embed the magnet in a dewar full of liquid helium. And it probably doesn't make any sense to do it differently, even if it were possible.
You need some mass here for the helium anyway as you never ever must run dry and it constantly evaporates.
I'm guessing that capture and reuse probably would add way too much to the price of the machine.