IMHO it’s more the organization than it is the GM. The inability to make a deal especially for a quality defenseman dates back way further than Holland. It should be quite evident by now some teams have a harder time making deals than others do.
The usual suspects like the Leafs the Rangers the Bruins and the Bolts have always historically also had an easier time making moves that improve their team.
Teams like the Oilers the Sens and the Sabres among others have historically had a more difficult time making moves to improve their teams.
Everybody talks about the OBC that the NHL is and it looks like some teams are in and some are out. Some teams get help and some just don’t. The ones that don’t usually end up getting bent over no matter who is at the helm though.
The deal making also reflects the stability of those organizations, their ability to build an internal pipeline of talent and then use trades and other means to augment into competitive teams.
The Oilers sadly are into their fourth management group within their rebuild(s). At the back end of this debacle, Holland's been the little Dutch boy plugging massive holes on the NHL roster and to build up a shitty prospect pipeline despite past incredible drafting position, quality and quantity. Losing two-thirds of a veteran d-corp's core (Klefbom, Larsson) required a massive rejig while the elite forwards rocket into prime years. The d-corp is still well below the quality and diversity of defending talent required on true Cup contenders.
The Sabres, in your example, have actually turned their situation into a fast, developing team with the trades they were forced to make when their top talent wanted out of incompetent management. O'Reilly begat Thompson who is incredible and Eichel begat Tuch and Krebs. They've also drafted well with cornerstone defenders and forward with their lottery 'money.'
There's no help for any NHL team that can't help itself with smart, stable management and organizations. While those teams you mention fish for finishing pieces, the Oilers are still needing to plug big roster deficiencies to surround its super elite and the bought and paid for quality supporting cast.