Since the drives are full of ECC already, do UREs result from multiple simultaneous errors? Can that be fixed with even more ECC? I.e. if the errors are reasonably independent, you could change 1e-14 URE rate to 1e-18 or whatever you wanted, by just adding more ECC, in principle of size logarithmic in the size of the disk (though you might want to cache it in ram in such a case). That is how tape drives work, I think. The put ECC codes into blocks on the tape, then erasure codes over clusters of blocks, then more erasure codes over clusters of clusters, etc. RAID amounts to doing that over entire disks, after all.
I think UREs due to problems with medium (magnetic layer) can be eliminated to arbitrarily small rate with more and better ECC. However I think (probably small) part of the total URE rate are randomly occurring errors due to intermittent mechanical and electronic failures, mostly due to random environment influences. Eliminating those would require technology improvement beyond more ECC on the platter. Probably more ECC and higher quality of all components along the whole datapath.
Maybe the above is wrong because UREs are just the unrecoverable medium errors. I can't find the official definition of URE rate.