[lucozade]

Your naive approach would work if 1) the possible projects match identically the resource profile without overlap and 2) there aren't any more possible projects than the set that match the resources ie there is no prioritisation decision to be made.

Unfortunately, that never, ever happens ever. So the organisation needs to have a mechanism for deciding how to prioritise work and to estimate what work can reasonably be done simultaneously given resourcing constraints. And it looks like you've described their approach to those two things.

The approach you describe sounds reasonable for a medium sized company assuming the quarterly process takes into account on going projects ie they're identifying and scheduling for resource gaps rather than fully re-scheduling every quarter.

A more common approach with that size or bigger is to use a budgeting approach. So notional dollar values are assigned to projects that are given priority and the project owner funds resource from other teams by giving them budget.