Because it was random and unprofitable for anyone. Besides, the old mechanics would throw random pirates at you in the middle of Pacifics.
What I meant was to make estate serving as a pirate hub, which not only would allow your AND OTHER corsairs to use it as a base (because lets agree, currently it is VERY obvious who employs corsairs), but would limit the number of ports accessible to corsairs and make those who host them partially responsible for all piracy (and could, for example, demand to close pirate ports in peace treaties, which would make them inactive for a while).
It also allows not only to spawn a number of neutral pirates who would make unknown to the enemy the true numbers of their fleet in the region, but also make a number of events.
For example, you said that small nations suffer from it more than others. But what if they had an option to choose to pay to the corsairs fee to pass and trade? Of course it would be scaling and not appliable to the local leaders/sea empires - at least not at a cheap price. This could be used to increase dev of the pirate port, making a benefit to the hosts of the port - for example, as a Britain if you're an underdog in Carribean trade you would probably win more from spawning more piracy and harming Spain. Same applies to France and others. I know that it would be kinda nerfing Spain, but... it's not like people don't question the current balance anyway, so why not include pirates in the equation?
Another thing would be that in a region like Carribean pirate ports could spawn spontaneously and once spawned, it would take some effort to close them. So, such a port would be also a source of unwanted problems, tolerated by the fact that it at least brings income and harm to enemy.
And it keeps 2 features of the previous models: dangers of random threat and the fact that the threat is controllable. Not to mention that once your fleet will be able to swim in pirate ports of other countries, you will gain a rather sweet anonymity. Of course, it's not like you will be unable to guess who is behind the pirates, but it would be a rather good way to establish "fog of war" for such regions. And there is a precedent of pirates going to war on the side of certain nations, so it is very plausible. And... it is done via the existing mechanics, estates. Which means that amount of things that should be added would be not that big (for example, current Cossack estate shows that a lot could be done with estates).