James Dumay, this would be extremely helpful for us as well. We heavily use pipeline jobs, and modify them often through the Job DSL plugin. Since the re-run button currently does a replay, it will use the old pipeline script instead of the latest one. The rebuild plugin does some nice things as well such as maintain the same build parameters and causes. Causes are especially important to us because it can trigger different behavior based on what caused the build in the first place.
IMHO, I think we should either have two buttons available in blue ocean - one for replay and one for rebuild, or, since the replay doesn't actually let you change the pipeline script yet through blue ocean (AFAIK) and the rebuild plugin truly redo the current build exactly as it was the first time, I vote that if the rebuild plugin is present, make the re-run button trigger a rebuild instead of a replay. I would prefer the latter since it prevents confusion, but would be a potentially breaking change for other users.