A public library streaming/digital lending system

I had an idea for something that could be cool.

Libraries can lend out any movie, CD, or book because of something called the first sale doctrine. This allows for the purchaser of any media to lend that item to another person.

My streaming box for Netflix/Amazon Prime broke a few months back and I procrastinated on getting a new one until I decided to not get another and try to get back to reading more at night instead of watching TV. I love movies though and remembered that the library has a surprisingly good selection, so usually on Fridays I'll go pick up a few to watch over the weekend. For new releases they often have multiple copies- the Bluebonnet location must have five or six in circulation. In this way I've managed to continue watching new releases/ classics, while cutting out a lot of crap I would settle for streaming.

Would it be viable for the library to create and offer an online streaming system available to the public? My thinking with regards to the first sale doctrine is that with the arrival of digital copies a portion of the money going towards DVD purchases could be diverted towards purchasing digital copies for circulation.

You might ask, "Why?" Well an annoying amount of dvd's /blurays the library loans out have been well-worn or damaged, resulting in many being unwatchable. A digital copy would never "wear down" or degrade in quality. Same for CD's of audio books or music as well as digital books. A digital copy never sustains water damage and the loan period would expire automatically, so their loaned media would always come back punctually.

The main stipulation that I think could make this work would be that the library would be restricted to only loaning out for streaming the same amount of digital copies as they purchased.

Are there laws respecting digital media being used in this way?