Each night at 9:30pm, I set 'do not disturb' on my phone, assuming all guests have arrived and we've exchanged a message or two so that I know they have what they need until morning. The upside is my sleep does not get interrupted by a reservation request or booking notification. The downside is that I won't get a message from a current guest that has an unexpected issue with the heat or what-have-you.
While it might be a nice enhancement to the Airbnb app, I would personally still struggle with having to remember to disable notifications. With an iPhone, I can program it to turn off all notifications automatically at a set time every night (and likewise turn them back on in the morning).