DNA mismatch repair enzymes repair mainly bases on the newly synthesised DNA strand, using the old DNA strand as a template. If the mismatches were simply repaired without regard for which strand served as template, would this reduce replication errors ?

if the old strand were repaired using the new strand that contains replication error as the template. Then the error would become a permanent mutation in the genome. The old information would be erased in the process. That is why, if repair enzymes did not distinguish between the two strands, there would be only a 50% chance that any given replication error would be corrected