It's actually required by law in most countries for people above a certain age to carry ID. The US is lax when it comes to ID laws so Americans who aren't driving may not be used to it. For international Disney parks:
Tokyo - Foreigners are required to carry valid passport or residence card at all times. If you don't have it, you can be escorted to a police station and forced to wait until someone reports you missing and/or brings your ID but in practice, this is unlikely unless you are drunk or suspected of doing something illegal.
Paris - By law, you are required to have proof of identity which can be a passport or other ID card. While you can be arrested if police ask you for ID and you can't provide one, in practice, you will be requested to return to your hotel and prove your identity within a certain period of time.
HK - Required by law to carry ID. If you don't have ID and are stopped by a police officer, you can be arrested and held for 48 hours. This happened to foreigners quite a bit starting in 2019. I have been stopped by police in HK but not asked for ID in that particular encounter. They did try to accuse me of littering by pointing at random trash that wasn't mine though.
Shanghai - Foreigners required to carry valid passport and Chinese visa (or residence permit) at all times. Will likely be arrested if you are found by police to not have it but how long you are held will depend on the mood of the police at the time.