There's a very simple reason not to varnish - the plate was incorrectly exposed but looks pretty good as-is, whilst varnishing it would detract from its look, i.e.: kill the brights.
The old literature also mentions that tintypists and others at big events didn't have time varnish (for some odd reason - I would have thought it was quite a quick process, but maybe some sandarac formulations took too long to set - I've seen some that have impressions/marks/defects in the surface that were obviously caused by them not having been dried sufficiently before being put into purse or pocket). Rob Kendrick cites this somewhere.
Sandarac isn't the only way to go either - the CWR forum has a piece about the civil war where tintypists were gathered around the soldiers and taking pictures, it mentions their "amber beads" and chloroform - it's a varnish as old as sandarac: not as tough, but it hardens fully almost immediately. And there were others - plenty of others, using lac, dammar, copal and other gums/resins.
BTW, another thing about sandarac varnish is the fact that nowadays it is used on a warm plate, sometimes it is even warmed itself. Towler (author of the pretty definitive text "The Siver Sunbeam") quotes it as being applied cold. A cold varnish on a cold plate. Maybe the plate was only warmed in the first place to dry it? Who knows. I suppose it would have taken even longer to set-up used like that.
I guess that JC and the rest of us were not around in the latter part of the 1800s, or we wouldn't have to reinvent a process that was so well documented back then.