Oh yes thats very true. And you are IFATC so you have much more experience in this then I do. Eyes on the ramp is what you need to do to see potential conflicts as you’ve mentioned. But, in my experience, eyes on the ramp to identify a call sign is a bit slow of a way. That may be due to the slow switching on call sign/username as the OP has suggested. Also it can be a issue when there are too many aircraft in a area to where the actual labels interfere and disable one or the other.
So my suggestion was mainly to yes, use the tower view to find actual aircraft, but to also use the map to tap once to see the label of a aircraft. It may be a situational awareness issue, where you are controlling a airport that you are not familiar with, and cant necessarily put where that aircraft is on tower view, onto to the map.
I’m certain that whenever a aircraft sends a transmission, that aircraft on the map blinks yellow to let you know what aircraft sent it. There you can see if its a pushback, etc. That’s how I use the map and is a recommendation to the OP.
I think someone on expert server controlling has the luxury to take time to use the tower view to find all aircraft who send transmissions on the ground. Because you have the commands and the ability to ghost someone who is excessively spamming the frequency with pushback notifications. Verses someone on training who may get kicked out for not responding to a request in 60 seconds because they are busy using tower view to identify every single aircraft who transmits a message. Not saying that is what the OP does. And also dealing with impatient pilots who expect a response the moment they send a message.