Nice idea. In fact, the department would own any NFA weapons. Upon retirement, an individual police officer would not be able to have one (called constructive possession). In principle he could use one under department auspices. In some states like mine, retired police officers are not automatically granted a carry permit for their pistols so using an M/G would be under very specific circumstances like training.
The only way an officer could buy an NFA weapon is if it were registered by the department as a transferable which means the department is old, or they paid market rates for it after '86.
That 1986 law restricted ownership severely. The number of transferables goes down over the years as individuals buy them for their collections and the amount available is reduced.
There is a reason for this - the anti-gunners won. Over time, only the very rich will be able to afford them.