I did Police Dispatch for a while. Whenever there was a traffic accident, unless it was very minor, the whole board would light up with calls. Of course, we were taught to find out what each call was because there was always a possibility someone calling in right then could be calling about something else, somewhere else. And sometimes, we did put them on hold if they wanted to tell us something they thought was important. But the call usually went something like... "911. What is your emergency?" They'd say something like, "There's a big crash at (location we already have units rolling to)." We'd say, "Ok, we already have units en route to that." Usually, they say something like, "Ok, thanks." and hang up (because all they wanted to do was report it, and we've just told them it's already been reported). Or, they might say they have some info to add, then we'd put them on hold and tell them we'd be right back with them while we quickly screened the other 20 calls coming in. But yeah, if they didn't at least find out what the call was about before putting you on hold, that's not right.
Also, I'll preface this by saying my dispatch jobs are ancient history. The first one was with a small town PD and we had 6 or 8 lines on an office phone, one dispatcher on the phones, the other on the radio...period. We used 3 x 6 cards in slots in the dispatch console to keep track of calls and units. The other was at a brand new large PD facility during the infancy of Computer Aided Dispatching with 8 to 12 dispatchers working phones and 2 dispatchers working 2 different radio frequencies, each frequency covering about half the city, but the radio had the capability to go on both frequencies for hot calls. Interestingly enough, I was much busier at the big PD, even with all the help there, than at the little one. I give this info because I have no idea how dispatch is handled nowadays and what new-fangled "magic" dispatch equipment they have today.