I remember a long thing about that issue on a Stargate commentary once, talking about shows that did and didn't do 'boot camps' for cast to teach them basics like realistic looking weapon handling. You notice for example that Amanda Tapping never allows her weapon to point at a friendly even casually. Trek has always been rather less robust on this front, probably because most of their weapons look futuristic/alien enough to get away with it. Discovery's rifles look pretty modern day though.Tyler has good trigger discipline. Lorca possibly doesn't.
Plus it's also cos they're not a military.

Who isn't?Burnham looks like she's checking Tyler out.