Practice Diversions by military aircraft have been carried out at both Military and Civil Airfields for many years. If one was to suffer a Real Emergency whilst in the vicinity of BOH it might help to be aware of what Type of Instrument Approach would be available. BOH Air Traffic Controllers may also benefit from the experience dealing with fast moving traffic.
I would say there are not plenty of military airfields left now either.. Count them!
Finally, what makes you think that Loud Military Aircraft do not disturb anyone at military airfields. Strange idea
Practice diversions, using BOH as a diversion airfield for Yeovilton makes sense. As I'm sure you're well aware, noise complaints from residents living near airports are more concentrated and powerful than in past times, when ironically passenger/cargo aircraft were very much louder. The penalties for exceeding certain noise levels and certain time curfews are not without a sting for the operators, so they aren't transgressed without good reason. The laws covering military airfields are different due to the need to operate 24/7 if necessary, so anyone who lives in the vicinity would know and be accepting (in as much as they can't change the circumstances). Not everyone likes aircraft, or the noise they emit and especially not 'the sound of freedom' that might cause those of us here to scramble to get a look, the majority only want to see an aircraft when they need to go on holiday etc.