Actually not, at first 10" is not so big factor, IMHO!
But, a bad surveyor will remain bad for life, only a good one can progress!
0.5", 1" and 2" instruments are mostly used in geodesy and monitoring, for scanning, topo and similar work 5" are also enough, overhead.
In practice, as a scan technician, you will rarely close a traverse and calculated it according to a strict method. You will often left on a blind traverse.