No, the take away isn't to tie up multiple sets of finite resources. If you're going to call res, then call res. Rebooking is easy, provided that the flight you now need to go on has the same booking code available. When it isnt, choices have to be made. Take the earlier flight in Y, or wait for the 1st available with inventory in my booking class. "An issue" could refer to an issue where the carrier is unable to deliever, in which case some rules are relaxed, or an issue where something has prevented you from taking your flight, in which case, many rules would apply. In the former, It's relativly easy (at least for me), in the latter, it can be well beyond my current knowledge in the systems we now use and the training I have been given.

Beyond using multiple sets of finite resources and being disrespectful in the etiquite of talking on the phone while talking to another service provider, when more than 1 person is making changes to a single PNR, very often, the "simultaneous changes" error comes up (if at the same time, it should come up 100% of the time) causing all of the work to be void and the people will need to start over, at times, the inventory you want is now gone due to the delay in processing.