After what happened to the two Italian Marines who were arrested by Indian authorities and the impact of that on a whole range of issues, including Fincantieri's bid to provide propulsion for the new Indian CV, states are a bit leery of providing service personnel.
AVPDs were used by EUNAVFOR ATALANTA including our guys at one time but these were assigned solely to World Food Programme contracted ships running into Mogadishu. Some countries did provide national elements to ships under their flag under purely internal arrangements.
PCASPs can be an excellent solution and, to be fair, I would say that the majority of companies provide a professional service. Much also depends on the Master of the vessel who retains overall responsibility but I think that the real solution is to provide hard rules at IMO level and a programme of auditing similar to that applied for ISPS. Fact of the matter is that with the sheer number of vessels out there, most medium-size European navies could spend all their time doing nothing but AVPDs if military personnel became mandatory. I understand the reaction of uniformed or ex-uniformed personnel to the use of armed civilians but we've done the same with banks, cash vans, airports and a whole range of other things. The days (and budgets) of States providing cradle to grave security are long gone.