Sort of! Beavers build dams as an instinctive response to the sound of running water.

If you have pet beavers in your house, and down put a phone playing the sound of running water, they'll start dragging stuff over to where the phone is.

How common are beavers as indoor pets ?

In the US at least I don't think it's legal anywhere without a permit. I've seen videos like op has posted, it's usually rescue animals being looked after not actual housepets

Never going to be common if their fate is to be like Peanut the Squirrel or Fred the Raccoon out of NY.

Relevant video https://m.youtube.com/watch?v=-ImdlZtOU80

Adorable critter with strong opinions on the arrangement of blankets and stuffies in a hallway. Side-recommended videos also lead me to Ze Frank's "True facts about Beavers" which is always a hoot. :)

Somewhat unrelated but maybe not.

https://www.hundredsofbeavers.com

Dam building as an instinctive response is kind of insane the more I think about it. What evolutionary pathway led to that behavior?

Attempted rationalization: Some proto-beavers with sensitive hearing disliked the sound of running water, and discovered they could shut it up by dropping stuff into the stream to plug it up. As an unexpected side effect (evolution cannot expect anything), the deeper water created gave them an increased chance of survival and the behavior spread as they out competed other proto-beavers.

The ones that didn’t do that tended to die before they could pass on their genes.

Tongue in cheek, the instinctive response of government institution employees used to be also to produce a lot of cellulose (here: paper) and pile it together.

You could try to airdop them to wherever they are needed.

Worked for Idaho: https://en.wikipedia.org/wiki/Beaver_drop

This article has a video: https://www.theguardian.com/us-news/2015/oct/22/idaho-histor...

There are various methods. A lot more around preventing dam building where it would be problematic. Things that block preferred locations either become part of the new dam, beavers destroy them, or sometimes a dam is created elsewhere.

It's probably not worth it if you want a specific dam location though. For general water retention we already trap and relocate beavers and just let them do their thing in the new place.

https://www.fs.usda.gov/Internet/FSE_DOCUMENTS/fsm9_032447.p... - Working with Beavers

You're thinking backwards! Environmentalists doing restoration work on former wetlands will often look for historical signs of where beaver dams had previously been and rebuild them. Beavers have a very keen sense for the ideal location to build dams.

Estimated beaver populations was around 200 million before "beaver hats" became a craze of Europeans that led to populations being hunted down to less than 10 million. It's hard to understate how deeply landscapes in North America were shaped by beavers

You'd probably have to go through a similar set of bureaucratic steps to get that done.