Sure, you won’t run out of names using bfpo4pkefistc1polh45ga3ndsz2o57.ui.nabu.casa, and it definitely is neutral enough not to offend anyone, but why not use something like Docker’s generated container names, maybe even with a smart home theme being hinted at?
Users could keep generating until they land on one they like, and they would be memorable, personalized, more fun, less confusing, easier to use, and align with HA’s goal of being more approachable. While my examples are basic, with the right word lists there could be enough for millions of URLs. Adjective/place/home-things could go on for a long time. This doesn’t do away with the custom alias option, but makes the default more pleasant.
Personalized name by user’s choice would be even better/only logical idea. Many (if not all) dns providers allow you to choose your own name. It’s impossible to remember nabu casa’s name, not in a million years. Just think that you’d have to re-setup your phone while you’re not at home and you don’t know your HA’s dns name…
Favorited or bookmarked it can be synced across all browsers and it can always be found by signing in to nabucasa.com, but still…there’s no good reason for it to be coarse and slightly brutal to remember.