It’s much more about naval control over the Bite than fishing rihgts, and the Worthless War came about in the wake of a series of naval conflicts between the North and the inhabitants of the Three Sisters:
“Even before the coming of the Andals, the Wolf’s Den had been raised by King Jon Stark, built to defend the mouth of the White Knife against raiders and slavers from across the narrow sea…During the wars between Winterfell and the Andal Kings of Mountain and Vale, the Old Falcon, Osgood Arryn, laid siege to the Wolf’s Den. His son, King Oswin the Talon, captured it and put it to the torch. Later, it fell under attack from the pirate lords of the Three Sisters and slavers out of the Stepstones. It was not until some thousand years before the Conquest, when the fugitive Manderlys came to the North and swore their oaths at the Wolf’s Den, that the problem of the defense of the White Knife—the river that provides access into the very heart of the North—was resolved with the creation of White Harbor.
…The last isles to be wedded to the Vale were the Three Sisters. For thousands of years, these islands had boasted their own cruel kings, pirates and raiders whose longships sailed the Bite, the narrow sea, and even the Shivering Sea with impunity, plundering and reaving as they would and returning to the Sisters laden with gold and slaves. These depredations finally led the Kings of Winter to send their own war fleets to seek dominion over the Sisters—for whoever holds the Three Sisters holds the Bite.”
So it’s absolutely the case that the Three SIsters *used* to be pirates and slavers, and shifted to becoming wreckers when more powerful forces cracked down on them, although they clearly still do a bit of piracy, because Stannis hanged twelve Sistermen for piracy when he was Master of Ships.
As for attempted invasions, well, where do you think Osgood and Oswin Arryn based and resupplied their ships from when they attacked the Wolf’s Den?
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