So I had this same desire, and figured a way around it. This will work as long as what you want to paste on multiple pages will be in the exact same spot. I set up where I wanted the pasted item on the first page. Then pasted it to the master page. It instantly pasted to all the pages. This would also work if you want every other page, just page that item to the set master page of those odd or even pages.

Also, to fix this issue in the future, I created an InDesign file of the thing I wanted pasted. What changes annually is just the date. So that date file can be updated once, then when I open the other file that has it on the master, ALL the pages are updated immediately.