They let you save on both shelf-space and money. They let you check out books that you're not sure you want to buy. They let you research lots and lots of stuff.
And they help keep your TBR pile lower because they will, in due course, be due back, and you may or may not eyeball them wondering whether you should renew them, but even if you do, you may decide -- nah. This can be wise when you overdose on an era for researching purposes.
OTOH, the reading/writing trade-off looks harder when you know that you will take back the books in a few weeks.