I apply a strict rule of:" If it is not not written, it does not have it." Period.
D&D 5e's monsters are
never listed with Tool Proficiencies. Do none of your NPCs have Tool Proficiencies, then? You know that the official Pirate Stat Blocks in D&D 5e (from Ghosts of Saltmarsh) aren't listed as having proficiency in Sea Vehicles, right? The NPC stat block for Bards isn't listed with instrument proficiencies, either. So, by this very rigid and close-minded code that you've for some reason adopted, in D&D 5e, Pirates literally cannot sail the ships that they use to do their pirating, and Bards can't play the instruments that they need to be, you know,
Bards. Is this how you run your games?
None of the monster stat blocks for Wizards before has listed their spellbooks, either. Does that mean that Archmages don't have spellbooks in your games? Most monsters don't have sections describing their equipment besides those relevant in combat (magic items, armor, weapons). Are commoners in your games all completely naked all the time, because they're not listed as wearing clothing or armor?
Or do you have your own special, homebrew version of the 5e monster stats that includes an extra line for tool proficiencies and a huge section for every single piece of equipment that the NPC has on them?
If you answered no to any of these questions and your games aren't filled with cities filled with hundreds of thousands of completely naked commoners, wizards with no spellbooks, bards with no instruments, and pirates that can't sail . . . you don't actually follow that strict rule you say you follow.
Clearly, the base assumptions of 5e do not follow this logic you claim to follow. It would make the game worse if it did, in my opinion.