It goes both ways, usually. If your defenders can't get the puck cleanly out of their zone and have no outlets, as well as being forced by their "fast system" to move the puck up the ice at all costs, you're going to get exactly what we've been seeing. This playstyle is also causing dmen that can actually skate like Montour and Fowler to try and do too much. The forwards are always way too far up the ice or clogged behind dudes in the neutral zone, so instead of trying to make another failure area pass they dangle through traffic or along the boards and make sloppy turnovers.
Our forwards are also so bad at keeping possession that our defenders are gassed playing high stress minutes in the d-zone rather than contributing to the flow of play. Lack of NHL forward talent on the roster obviously isn't helping this, but I honestly think Carlyle is just in over his head. If you don't want to play dump and chase, you need personnel that can regularly carry the puck into the offensive zone without having a panic attack. The only forward on our roster with the speed and puck handling to do this regularly is Rakell, and then his next pass is immediately fumbled by the receiver or nobody is open and it gets tossed along the boards never to be seen again.
Until we get better coaching or better players back from injury, we're kind of stuck in the no man's land that we've been seeing. Our forwards aren't skilled enough to play an uptempo/clean passing game, and they're not physical enough to win puck battles and grind it out in the dirty areas.