I have traveled four continents over the past 30 years and have never been a victim of a crime until 2013 when I visited Providenciales in Turks and Caicos.
After locking our rental villa on. Grace Bay in November, 2013, my husband I went out for dinner. When we returned our unit had been ransacked and everything of value STOLEN. We called the police and officers took a report. After we returned home I have tried numerous times to contact the TCI police and NO ONE RESPONDS. We are left to believe that they do not value tourists and that they regard us as just out of luck. I realize that crime happens, but one hopes that there is a responsive police force to at least answer a victim's questions.
If you visit TCI, be forewarned that of you need help, you Cannot rely on the RTCI police force. One only needs to read the local papers to know about the many problems plaguing their police force. Yes, it is beautiful there. But , you might want to consider visiting some other beautiful place which has better public safety officers.
There's nothing unique about you unfortunate situation, the disinterest from the authorities is quite common when it's only property damage and no physical threat or injury occurred. You'd be treated a LOT worse in most similar destinations.
There is a fair bit of crime on Caribbean islands where many are unemployed or poor and they daily see rich tourists there.
People do die sometimes from crime in the Caribbean, but murders are quickly hushed up as they are bad for the tourist industry.
As a tourist anywhere, you are seen as a visitor for a week or two then will probably never come back, especially if you were robbed or attacked, so the police will make some noises but will do nothing as they do not consider you worth the effort.
Often the best you can hope for is a police report which you can use for an insurance claim, assuming you have insurance.
"We are left to believe that they do not value tourists and that they regard us as just out of luck" You are clearly new to travel. You will be hard pressed to find a competent third world police force, especially in the latin world.
I am not new to travel, just new to crime. I have been to at least 24 Caribbean islands and return to my favorites year after year, this was my first visit to Providenciales, but it is British, so I guess I expected a police force on par with Bermuda. Wrong.
I am posting because I am someone who exercises reasonable caution when traveling and assumed that a place that survives on tourism would make reasonable efforts on behalf of tourists. Maybe others can benefit from my mistake. A place may look like paradise, but beware.
"... assumed that a place that survives on tourism would make reasonable efforts on behalf of tourists... A place may look like paradise, but beware..."
You just described most of the Caribbean and all of Mexico and Central/South America.