That's exactly what happened.
Ship owners invested in arming their ships to the point where the pirates would hopefully pick softer target which is exactly what they did. Incrementally over the 16th-18th centuries the profitability of piracy was highly reduced because the goods had fairly fixed relative value and the risk kept going up and it more or less went away on its own in the Western hemisphere over the course of the 18th century. Crime rarely pays at scale when every instance carries a high risk of a firefight. A few may make a good living in such an environment but it caps the maximum industry size at a very low level.
Piracy persisted in the Mediterranean where it was more or less a state sponsored activity. They mostly avoided harassing the commerce of major powers (Britain, France, etc). Which worked well enough until the 2nd tier powers got pissed off enough to stomp them a few times (with the blessing of the first tier powers, think of it like a reverse Falklands). They still didn't tone it down sufficiently and they wound up speaking French for that mistake.
If anyone has any good resources on the history of Indian ocean or east Asian piracy I'd be interested in reading them.
As an aside, old school high seas piracy is an surprisingly good parallel to the variations of criminals in the current cyber-crime environment. You've got state sponsored theft of money and goods (privateers). You've got under the table cyber criminals who would be prosecuted by their home jurisdiction if found (traditional western pirates, the kind you typically see portrayed in pop culture). And you've got locally approved as long as they pay their dues professional cyber-criminals (north african pirates). The former groups mostly steal things of value they can use or fence. The latter mostly takes stuff hostage for ransom.