Your DH is incorrect to say that everyone prefers AI.
I've never done all inclusive but have stayed half board and B&B in a hotel that offers it.
I can see the attraction if you want to eat and drink a lot or want to fix what you spend in advance. They also offer entertainment in the evenings and kids clubs and activities in the daytime. We also make sure we get a balcony or terrace so we can sit outside in our own space.
However, the first time we went HB, I realised that one thing I like to do on an evening is go for a wander, a drink and tapas or a meal outdoors (we always go to Spain and its islands). I wouldn't do HB again for this reason as I didn't like the evening buffet. I do like the breakfast buffet though, but I think I have decided that our next holiday will be self catering in an apartment (just a couple so a villa would be more space than we need and expensive).
The other thing I have decided that I don't like about hotels is maid service. I don't see the need for the bathroom to be cleaned everyday and feel bad that it has been left in a mess and made this difficult for them. I also don't like how they make the beds and pile them up with cushions
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I don't know where you are looking and I have only holidayed in Spain. I don't know if it is different in Egypt/Carribean etc. I would do AI if the hotel restaurant(s) offered table service outside on an evening, but not otherwise.
With SC in a villa, you don't need to cook all the time (BBQ, takeaways, eat out, simple food) and when we have SC in the past, I have never done any cleaning during the holiday apart from keeping the kitchen usable - always get a dishwasher - all other cleaning and tidying is left until leaving day.
I would also see the advantage if you have DCs is that you could put them to bed and then have a nice meal just you and DH in the villa, which wouldn't be possible in the hotel.