Superconductors also have points where they stop superconducting because of the strength of the magnetic field or amount of current. YBCO and similar have these points below the useful level for MRIs.
There's research around finding ways to use them but nothing that is currently viable.
You're right - for whatever reason I had convinced myself YBCO had issues with both high current and high field. It's just high current - anything outside of a single grain has low current density.
Doing some more research to help make up for my spreading of incorrect info, I did stumble across this - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5472374/ - it seems like it's a variety of factors that make most HST not really commercially viable for MRI machines at current.
There's research around finding ways to use them but nothing that is currently viable.