Marshall, please think again: if you have f.e. input a time signature by using the Shift-M popover, you confirm your input with Enter.
If the popover would now stay open - as you suggest - you could write another time signature on top. Why would you want this? It does not seem to make sense - to me at least.
Triggering a popover is like you talking to the application, calling up a command. You have to confirm your task, then the task has been done.
If you want to call up a different popover, you can do this right away.
Do you suggest that there would be one type of popover only to collect all commands?