Haven't a few wars over the centuries been fought over barren waste lands? Although admittedly, they did involve resources at some level.
Or territory. Those barren lands have often been important because of their position, their value as, say, a route of travel and trade between two civilizations. The trans-Saharan trade route, for instance, was vital to Europe in building its wealth and power, since so much of that wealth came from the gold mines of West African empires.
But the abandoned Borg territory is mostly going to be so huge that powers on opposite ends of it may not even be aware of each other's existence. It would probably take generations for any trade routes across that wasteland to be established in the first place.
I wondered about that when "Scorpion" Part 2 aired. Janeway talks about how a weapon of mass destruction would endanger innocent worlds. Although it seems like there wouldn't be any left in Borg space anyway.
I figured Janeway's concern was for the inhabited worlds on the borders of Borg territory. There must've been tens of thousands of them at least.
Even if the former Borg systems in the Delta Quadrant are stripped and useless it seems like there would still be a lot of chaos. The major power of the quadrant is gone, somebody is going to want to fill that role.
Oh, definitely. Just off the top of my head, I can think of a number of ways in which the sudden absence of the Borg could be politically, socially, economically, or otherwise destabilizing to countless civilizations. I just think the specific idea of a "scramble" for former Borg territory wouldn't be one of them.
I suppose the Vidiens (sp?) are out of the picture since the phage has been cured. The Hirogen are probably taking advantage of the chaos with their usual hunting hijinx. The Kazon just don't have the tech to pull it off. The Voth seem like the most likely candidate to become the new major power there. Of course there are many races there that we never got to see..who knows?
The Kazon aren't particularly close to Borg territory anyway. With their technology, it's many years away.
As for the Voth, they're already a major power when they choose to be. But they have their own approach to wielding power, as I've touched on in Places of Exile and "Brief Candle."