I live in Virginia and I found multiple library systems that would allow me to get a library card as a state resident. For you, I just searched for a few nearby localities and D.C. residents can get a card for free. I'd just type in all the obvious systems near you and see what you come up with. It helps to have multiple library cards on your Libby app so you can join the shortest queue.

Here's a few to get you started (FWIW Fairfax charges $27/year for a non-resident card):

https://mcpl.bywatersolutions.com/cgi-bin/koha/opac-memberentry.pl

https://catalog.library.loudoun.gov/obr/

https://libcat.arlingtonva.us/MyAccount/SelfReg

Also depends how many copies of the book they buy.

It really varies. People can return them very quickly, since you can return it as soon as you're done reading. Or people don't actually read it and it sits there for 3 weeks.

If you live in the DC area, you can get a library card with neighboring counties and get on their waitlists as well. That means you can have multiple Libby accounts.

https://ggwash.org/view/65888/washington-dc-residents-can-get-a-library-card-almost-anywhere-in-the-region

Ebooks tend to take longer than audiobooks, which many people seem willing to listen to and then get off their phones. It seems that people keep the ebooks sitting on their kindle the entire three weeks.

Just got a DC Public Library card and placed a few holds on books with super long lines (30-500+)

How long do these queues typically move for eBooks?