We’re all works in progress, honey. And believe me when I tell you that I’ve had to work harder than most.
― Susan Elizabeth Phillips, "Ain't She Sweet"
It's pretty well understood that limiting Work In Progress - or WIP as it is often abbreviated - is a good thing. Ideally, WIP should be limited to one item in progress at a time. Having multiple pieces of inventory on-hand is a form of waste, since each incurs a handling cost, and any work done on one of them will depreciate while another is being worked on. In theory at least, restricting WIP to one item at a time will reduce this waste and get value out of the door as quickly as possible.
This principle of Single Piece Flow (SPF) is central to Lean-Kanban ways of working, especially in a manufacturing context. In a software context the accepted WIP limits tend to be rather higher. It is often limited to one item per developer, such as by allowing each developer only one avatar to place on an item, and it can be reduced further if pair-programming is in use. As such, software teams might not often achieve SPF but the value of limiting WIP as far as possible is still understood.
There are however problems in interpreting limited WIP in Scrum. This is because a Scrum board will often take the form of a task board ... not a Kanban board. In other words, the work being limited by Scrum teams is not always a user story or similar requirement. It is often a task.
Task-limited WIP allows developers to progress tasks from any user story in any order. They could potentially limit themselves to one or two tasks from a story, complete them, then move on to a task from a different story and maybe a task from a third. In effect multiple stories - perhaps even the entire Sprint Backlog of stories - can be in progress before so much as one story gets completed.
None of this breaks Scrum rules. There's nothing to stop a team, in Sprint Planning, from organizing the Sprint Backlog into any number of tasks which can be progressed in any order they choose, and from delivering all of the user stories in one go at the end of the Sprint.
The Sprint Goal can of course be met by this approach, and there should still be a nice task burn-down to show the associated technical risks being managed. The problem is that it defers approval of each user story to the end of the Sprint (i.e. the Sprint Review), when it is best-practice to get continual sign-off by a Product Owner throughout the iteration. On-going inspection allows the business risks of delivery to be managed well, and not just the technical risks.