Limiting your work in progress (WIP) has several benefits I can think of in making individuals and teams more effective
If you regularly have to switch between tasks to get something done, or worse still some outside force is causing you to constantly switch, it is much harder to focus on the individual pieces of work.
When there is a lack of focus, mistakes are more readily made or aspects missed from the work.
Reduction of work / thinking time duplication
When it comes to knowledge based tasks, switching between different tasks has a significant time cost associated with it. If you start working on some task that is going to take a half day to complete, but after a couple of hours have to work on something different, a significant amount of time is required to get back to where you were with the original work.
Working on one task until it is ready to pass on to the next stage gives better feedback on how long that type of activity can take. Better feedback helps you more accurately adjust any estimation you are required to provide.
Maintaining a good flow of work
Switching between tasks interferes with the flow of those tasks and can delay work being completed at the perceived time. Any planning and estimation done prior to the work may not be judged correctly if you do not include time wasted due to task switching.
If you minimise your work in progress and only work on one task at once it is easier to get accurate measurements of time required to complete each task, giving better feedback to your planning and estimation activities.
Avoid building a psychological mountain
If you have too much work or you see the work as to vast or complicated, there is a natural tendency to be overwhelmed or demotivated by the scale or complexity of the work.
Humans can process more work when it is viewed as small and not overly complex.
Technical Debt / Stale work
If you have a lot of work that is in progress, then the effort already invested into it has yet to deliver any value to the customer (in a personal Kanban, the customer may often be yourself). The more work in progress you have therefore means more investment without return of value.
In manufacturing, if you have a high investment (inventory) without delivering any value (sold products) then your business is not being effective.
In software development, if you have a large number of requirements (stories, use cases, etc) in various stages of development, then that is a considerable investment made without that software realising those requirements in the hands of the paying customers.
If you minimise the overall work in progress you have less investment and less risk should there be a change to the project.
There may well be other benefits to limiting your work in progress, but this is all I can think of for a wet Sunday afternoon. If you can suggest others, I would be most interested.