I do wear a snorkel all the time....trained that way. BUT, up until about a year ago, it was a royal pain for me. The snorkel strap would get tangled in my hair and hurt as the snorkel moved around while diving (relieved that some with a neoprene snorkel strap which I think also alleviated the slight mask leakage at the corner).
So with the hair pulling and slight leakage occasionally, I was thinking of not wearing one but just having it in my pocket. Even bought one for that purpose....THEN I started diving with a beanie and that solved two problems....no hair in my face, no hair near my mask skirt to allow leaks, no hair near the snorkel so no pain....that solved the problem for me. Although sometimes the snorkel does move around and get in my way a little bit, but the more I dive, the less it does that....or else it is the fact I'm just getting more comfortable with all the "stuff" on me and am desensitized to the snorkel bobble. LOL
I have used my snorkel for surface swims to dive sites off Maui and that was well worth it to save that air for the main event. Glad I had the added bottom time even if I did get a little snorkel bump every now and then.
So, I guess, until I get many more dives and a lot of experience in various conditions and environments ..I'll keep wearing my snorkel. Obviously, what might help you, ScubaMarc, is to try a different style and/or color (to avoid confusion if that's the problem) snorkel to see if that helps. When I switched to a different style (shape) snorkel that seemed to help me....just find one that works for you. You didn't say how long you've been diving so if you have a lot of dive/snorkel experience then maybe you've already tried my suggestions...but if that's not the case.......
ScubaMarc-surely your instructor will have several different styles for you to try....seems like everybody I know has at least two or three different snorkels somewhere in their bag or closet. Ask around and try some different ones before throwing out the "baby with the bathwater"... Then you'll be able to make a knowledgeable choice that works best for you. Good luck!