We have been on 5 Disney cruises and on every one, the agent did not look or barely scanned our passports. However, each and ever time, my husband was asked "That's a nice watch, did you get that during your cruise?" He did not but they appeared to be more worried about customs allowance than ID. However it is a closed cruise and Disney submits all guest information in advance.
The last time we flew to England, the customs agent asked my daughter " who is this guy?" and pointed to my husband (her father). He was looking for the answer "my dad" but she got scared and said his full name - it was very cute and when we all started to laugh so did he. There were some more questions but when he got the right answer he let us go through.
They're very strict in the UK about travelling abroad with minors. Im American and I have two American sons that live with me in England. Every summer I take them back to the US to visit my exhusbeast. Most the time the boys get questioned, "Can you tell me who this woman is?" or "Where's your dad?"
Passports are indeed expensive. I have to get 4 minor passports every 5 years at $85 a pop. It's not an option for us not to get them. If we didn't have valid passports at all times we couldn't ever get off this island.