For the initial question: I work in non-AEA, small nonprofit settings. I just finished a show where I operated both sound and lights, it was a 57-page 100-minute play where the audience exit cue was SQ702 and there were at least 50 0-count LX cues. It was utterly ridiculous to expect a single person to have to run that. I really needed three hands (one for lights, one for playback, and one to mute mics, text the house manager to turn off the AC, and turn the pages). This show was crazy, and I really wish I could have just called it - or even if I ran one and called the other, that would have been fine too. However, I'm super used to it. It happens far more often than not, that I'm operating at least either lights or sound, if not both. Some day I'll grow up and work in larger companies and breathe a huge sigh of relief when I'm not pushing all the buttons too.
For SMeustace's question: Yes, definitely. There are some moments where it just won't work for it to be called. Maybe it needs to be absolutely instantaneous, so we can't wait for the lag (however tiny it may be, it's there) between the "GO" call and the actual go. "LX 52 on your visual right when the actor puts the hat on his head." "SQ 29 on your visual as the actress presses the doorbell." "LX 100, 105, and 110, on your visual with each kick." However, in these instances I'm still calling the cues, I'm just telling the operator that they won't hear the GO word from me, they'll see it on stage. The board op is not running it autonomously. I'm still telling them exactly what will happen on stage and what their response to that action should be. (See actress press doorbell, hit GO button in QLab.) I'm not in the dark on these cues at all - I know what's happening and when, it's just a situation where I can't be the one to call it because it really must be timed tighter than I'm capable of calling.