@scargirl Aside from most people working out in commercial gyms where it is strongly frowned upon to utilize more than two pieces of equipment at a time (and some people even frown upon that because they're afraid to say 8 words to a stranger to ask to work in), there is some science and technique to properly planning when movements occur in a workout.
If you don't care about optimizing your workout/gains and are trying to get through a workout efficiently:
The biggest potential drawback (imo) is pairing or tripling inappropriate movements and fatiguing muscles in such a way that you limit your exertion on more 'important' movements.
Even the example you used is, in my opinion, inappropriate.
I'd never do a curl (fatiguing biceps) before a pull/back movement because my fatigued biceps would negatively impact my heavier, higher intensity pull/back movement. Similarly, shrugs (which I personally find relatively useless and don't do at all anyway) are typically done with a relatively heavy weight, and so now your grip is being significantly impacted as you go through your sets too.
I find pairing antagonistic planes of movement (bench followed by row, or pulldowns followed by OHP, for example) to be a better way to save time without impacting performance on either one.
If you have an empty enough gym that you can feasibly be using more than two pieces of equipment at a time without someone coming along and stealing one of them (or pissing off people afraid to ask to work in...) I'd tack on some small isolation movement for a third muscle group or plane of movement... like do bench, row, calves or something like that. Something small enough and low enough intensity that it acts like rest time before hitting the two bigger antagonistic movements.
Just my .02.