Natively count all bookmarks in Firefox

Actually, yes, you can.

Thanks to this Mozillazine article: http://kb.mozillazine.org/Counts_-_Counting_bookmarks_history_links_and_other_data_-_Firefox

Open the Bookmarks library by pressing CTRL-SHIFT-B, then place ":" in the Search field to return all bookmarks.

You can now press CTRL-A to get the total count.