Good idea! Improvement stories are technically just a duplicate of the original user story with one or more acceptance criteria added. But duplicating the user story for every added acceptance cirterium would be verbose — improvement stories are a nice and hands-on solution.
In practice I see this used well by experienced agile teams. A word of warning though: it might not work as well with teams who are new to agility. I can see them evading writing user stories by writing everything as an “improvement story”. Requiring improvement stories to be linked to a user story will certainly help. I would just watch unexperienced teams more closely on that ;).
Again, great idea! Thanks!