I'm guessing pigeon-holing could be a problem for someone younger in service/planning to get promoted but tbh it's not been a major problem for DH - he's got 29 years service in and is still active (rather than office-based) so quite unusual anyway.
Like elsewhere, DH has found over the years that if your face fits, then transfer/promotions occur whatever, if your face doesn't fit, well you know the score.
His first inspector hated the agreement and tried not to recognise it; the next inspector wasn't given the correct info so tried to say he couldn't do it, but DH put him straight on that one. No inspector currently, but DH is flexible and sensible - if his co-sergeant is not at work for any reason he will do the full night, rather than half night which he is supposed to.
He still works full-time, and there are often variations to the shifts for operational reasons.
At the end of the day though, DH's health suffers if he works full nights, and his health is more important than how others perceive him.