This already exists at some libraries! Example: https://collections.biblioottawalibrary.ca/en/musical-instruments

my Library does that too.

libraries are just books, they have a lot of services, besides being one of the few places you're allowed to exist without payment.

mine has a maker space with so many tools, cnc, 3d printers, large format printers, sublimation printers, embroidery machines.... office spaces, rooms to book, library of things with telescopes board games, repair tools, music instruments...

please go check your local library and get a card

Already a thing in Finnish libraries. You can also borrow powertools for home fixing.

At our library you can borrow instruments, tools, toys and computer games.

Not a library, but the EMP Museum in Seattle has different soundproof rooms with instruments and recording equipment you can use to produce your own stuff.

Libraries sometimes have power tools or cooking equipment and all sorts of cool stuff. They are truly the best thing about modern society.

I like the idea, however there are some differencea between books and musical instruments. Hygiene is a problem with all woodwind instruments. Strings, sticks, cymbals, cables brake and need to be replaced regularly. Also a whole ass drumset is huge compared to a book. But there are rehearsal rooms that you can rent that also rent out instruments. It is expensive though.

Libraries can also do that.

My concert band does that. You can borrow an instrument and we arrange for cheaper tutoring. You just have to promise to play in our band a year later.

The local music school (the place where you go to get a tutor. Not a school for general education) and the local instrument store also lend out instruments.

or tools too expensive specialized or cumbersome to actually own.

As someone who teaches percussion and constantly has to deal with kids that I KNOW breaking publicly used shit, I can’t imagine the instruments would last long out in the wild. Most instruments require care and maintenance from someone who knows how to take care of it. Even on a day-by-day basis. 

If I look at how people handle CDs and Blu-Rays in our library I don't think it's a good idea. In theory yes, but people can't have nice things

My local library lends out cruising bikes 🙂

most schools offer this for kids.

and a lot of music places offer rentals.

A great idea.

Libraries in blue states in the US do that commonly. I hear, but don't know first hand, that it is less common in red states. I assumed europe did it too, but maybe they don't?

Couldn't you just go to a store that sells musical instruments and try them out there? I don't know enough about musical instruments to know the answer, but I am a hobbyist photographer and we can certainly do that with cameras.

My ideal "non-book library" would be a public woodshop with a Ron Swanson librarian figure to help people use the tools safely.

Woodworking seems so satisfying as both an art and a craft, but between the cost of materials, tools, and the space needed, I could never take up the hobby in the foreseeable future. But if I could go to a public workshop and use shared tools, just providing my own raw materials, the barrier to entry falls dramatically.