Do all airlines allow the BedBox™ onboard?

As a carry-on is should be permitted onboard any airline as long as it is covered by your ticket fare.

As a bed feature, most airlines have allowed the use of it and you can find a full list of these family friendly airlines here : https://www.stokke.com/ct/airline-list.html

Please note that the crew onbaord will have the final decision depending on the flight situation when it comes to the usage of the bed function.