It sort of depends on what you mean by the 'Golden Age of Piracy'.

Now, strictly speaking, the 'Golden Age of Piracy' usually refers to a period in the mid-late 17th century when piracy in the Caribbean was rampant, but piracy in this period is pretty different from most people's general conception of 'piracy', which is closer to the piracy of the mid 18th century.

In the 'Golden Age' proper, actually illegal rogue pirates were much rarer than they would be later on, but privateering, when a government contracts out private vessels to attack their enemies without the fear of being prosecuted, was incredibly common. The consequence of this is that, if countries aren't at war, it's really hard to make money 'legally' as a pirate. The 'Golden Age of Piracy', in this sense, ends with the Treaty of Utrecht. Pirates had traditionally preyed on Spanish ships (as they couldn't afford to defend them properly, but they were, ironically, loaded with valuables) and, with the UK and the Netherlands (and France) at peace with Spain, privateers became less popular. There are smaller wars between colonial powers in the next period, but they never last particularly long until the War of the Austrian Succession. By this time, however, the naval balance of power in the Caribbean has completely reversed: English, French and Dutch trade are really strong but their naval presence is lacking compared to the Spanish. In this period there are plenty of Spanish privateers, but they're not nearly as famous as their earlier English and French counterparts, so the 'Golden Age' as exists in the popular imagination seems to have passed. From this point onwards, governments become less and less attracted to privateering, and begin to legislate against it.

In the illegal sense, though, your analysis is pretty much correct: rogue pirates can't operate because the laws are better enforced. A big part of this was the Piracy Act, which allowed people accused of piracy to be tried anywhere in English territory, as opposed to only in England proper. This, naturally, makes it much, much easier to try and punish pirates, and so a lot of pirates leave the relatively well patrolled Caribbean for less-developed colonies, where enforcement is lax.