s it actually easier and cheaper to go for an all-inclusive for a week or do most people still find it better and cheaper to book flights and an apartment separately
That's not the comparison you need to make/think about.
You can book flights and an AI hotel separately or you could book a package where the accommodation is self catering and there's no rule to say that either method (package or individual bookings) will work out cheaper or more expensive.
We've had it both ways, especially with Jet2holidays, where we've had a package for very little more than the flight and the accommodation before you consider the cost of hold luggage or transfers.
You need to think about the comparison between SC and AI however you book it, but cruicially also how you'd feel about the food provided with AI, especially if it wasn't very nice/to your taste as you can get AI for not much more than SC but it will be 3 buffet meals a day and it might not be very good quality/to your taste.
I wouldn't go mid range buffet 3/4 star AI because I don't like buffets for lunch or evening meals and would be disappointed if the food wasn't to my taste as a big part of a holiday for me is being served local food at an outdoor table with a sea view or in a picturesque town square. You can get AI with a choice of a la carte restaurants, but it is very expensive.
If you're not particularly bothered about what the food might be like, you could go AI, or you could pay for the higher end AI, but then it's likely to be a lot more expensive than SC and eating out.
What we generally do is go SC or B&B in an apartment where you get a kitchenette and will generally have breakfast quite late, then eat out for lunch or dinner, but rarely both and for the other meal have either a big ice cream, or street food type thing out (empanada or slice of pizza) something snacky like bread, cheese, olives, crisps etc, or a barbecue, or pizza from the supermarket, that sort of thing.
Probably works out cheaper than high end AI, but a nicer experience than buffet AI, plus minimal cooking and I love a nosey round a foreign supermarket. We always make sure we're walking distance from at least a decent sized convenience store so we can stock up on fresh bread, drinks, ice creams, snacks and easy meals/BBQ stuff.