Firstly yes the police can deal with the breach.
Undertakings are usual unless there has been actual violence.
Personally I prefer undertakings as opposed orders due to enforcement.
As you know you cannot have a power of arrest on a NMO. If there is a breach you make a complaint to the police and it is hit and miss at to how the police deal with the matter - as you have discovered.
If the police do arrest and charge him with breach of a NMO the matter is dealt with by the Magistrates Court and unless it is a very serious breach often result in a fine.
If however he breaches an undertaking you apply to the court him to show cause why he should not be sent to prison.
I would much prefer him to have to go before a judge at the Family Court to face any allegation of breach rather than the Magistrates Court.
Of course it would be for you to make the application as opposed the police / CPS dealing with it if it was a breach of an order but as I say a judge is likely to be tougher than a Magistrate.
So there are advantages to an undertaking.
Also if a criminal conviction for breach of a NMO impacts on his employment it could then impact on financial support you receive or should receive if he loses his job.