You could "almost" do things this way. Unfortunately, you'll have to occasionally wipe the "mirror" systems.
If I restored a full to the "mirror" machine, followed by a differential, followed by any number of incremental backups, there's almost a 100% chance that files which were deleted since a previous backup will now be present on your "mirror" machine. Since a restore from backup won't wipe out files on the system which aren't on the backup, you'll always have some percentage of "cruft" on the "mirror" system which should not be there. If these day-to-day work files are not a concern, and won't interfere too much, and the "mirror" system works, but isn't perfect, this solution is better than having nothing, and would have you up and running quicker than doing a BMR after the incident.
