In true HN haven't RTFA (apparently Cloudfare has banned my IP address from the APS's website for overuse...) but even if the critical surface of Bc / Ic / Tc is similar, there can still be a massive engineering advantage to a new material for other reasons.

One of the major difficulties with manufacturing large magnets out of existing technologies like Nb-Ti or Nb3Sn (which is used for ultrahigh field) is the welds. You need O(100 km) of superconductor with no defects embedded in a copper or bronze matrix (for taking the quench current and mechanical support). As you probably know, these are made by taking a block of copper (or bronze), drilling out holes in it, putting in rods of e.g. ultrapure Nb3Sn in Nb sleeves, and then drawing it under very controlled conditions. The metals have to be pure because work hardening around defects is definitely a thing, and you do not want an unknown break in the wire, ready to become resistive and take O(0.1-1 kA) currents.

This is "specialised" to put it mildly and joining a broken wire is somewhere on a scale from impossible to bloody difficult -- traditionally think lovely solutions like Piranha or HF, and words like "cold welding". Only recently have people started to get TIG like hot welding techniques to work -- but then you have a difficult problem anyway because it is analogous to joining something like a 28 core cable where one dodgy connection can cause what is effectively a controlled explosion.

In applications like NMR or MRI you still want to cool down your superconductors as much as possible even if they can handle higher temperatures. As far as I understand this still increases the amount of current they can handle and so increases the maximum field.

The largest commercially available NMR spectrometer has 28 Tesla, and that is a hybrid magnet with both conventional superconductors and high-temperature superconductors. And it's cooled with liquid helium.

High-temperature superconductor refers to the critical temperature at zero field. But the crucial field decreases sharply with temperature, so the superconducting phase appears concave on a T–B phase diagram. Therefore, in order to operate superconducting magnets at high field, liquid helium is necessary irrespective of the superconducting transition temperature (critical temperature).

Yes, they operate at 4.2 K (liquid helium temperature).