I've had minor problems having the kids on separate bookings, but none of them serious enough that I'd change my means of payment just to have one PNR. Problems have included, for example:

Forgetting to uncheck the automatic "request an upgrade" on the parent's ticket purchase. That's a fairly easy fix if the upgrade comes through and separates you from your child.

During an interrupted flight once, my 3-year-old child and I were automatically rebooked on two separate flights. A quick conversation fixed that. (Computers can't see the linked notation on the PNRs.)

During an equipment change once, our seats were separated on the plane. The gate agent fixed it.

The more children traveling and the more PNR's you have, the more difficult it can be to manage when there are disruptions. Four kids and one adult all on separate PNRs could be a nightmare, for example, to coordinate, I can say from experience. But very often it's the only reasonable way to book the tickets because of different starting cities and travel dates dependent on the school holidays in several different school systems. One needs to stay vigilant and proactive, but it's usually not a big deal.