From what I can remember about one of the recent accordion "heists" in the UK, the premises had been visited on at least one previous occasion by two Eastern European types who made enquiries about accordions for sale. They were "captured" on CCTV, although I'm not sure if they were ultimately identified. Even if they were, where do you start looking in an area of free movement like the EU, especially if they have been away from their country of origin for some years and all the local cops can tell you is that they are in fact well known, but "believed to be currently residing in Germany", or wherever.
We once had a very well known gang of criminals in the Edinburgh area who called at rich people's houses in smart suits and posh hired cars (hired using stolen identity documents), and purporting to be home improvement agents. After they had ascertained when certain people would be absent from their homes, other members of the same gang would turn up with removal trucks and empty the houses of everything of value. Any antiques disappeared quickly to the south of England, for onward conveyance to the continent, where they were sold before the local police knew anything about the items concerned. The break in would not typically be discovered until the occupier(s) returned home some days or even weeks later.
The faces of the callers were certainly recorded on CCTV, and they were all very well known to the police, but it was impossible to prove that they were linked with any of the housebreakings, as they never broke into the houses or handled any of the articles removed. With regard to the hire cars they would make sure somebody else called to pick the car up so they couldn't be identified by the hire company, who would also have been given a cash incentive not to cooperate with the police. No DNA, no fingerprints, nothing. Those people do that for a living and cannot afford to get it wrong, so they become very clever at what they do.
I would imagine professional musical instrument thieves would tend to operate in much the same manner. Hopefully any insurance company involved will be sympathetic to the lack of security arrangements at the premises concerned.
