The plane ticket was the most expensive part at about $1.2k iirc. If you planned ahead better than me it's not hard to find $1k or even a little cheaper, granted I live in a city with an international airport so ticket prices also tend to be a bit cheaper here. A family of 4 could do $100/night hotels and get places much nicer than what we did and have enough room. Food costs are so low in Taiwan we stopped even tracking it. Maybe if you only want to eat at fancy sit down places in the center of Taipei or something food would start to add up. I'd high end estimate $10/meal/person but realistically it's like half that
So say a family of 4 over a week, that's $4.8k plane tickets, $700 housing, $840 food, total for all big purchase estimates here is $6,340. Cheaper tickets readily knocks $800 off without putting much effort into hunting for deals, another $400 off for food if you aren't being fancy with it every single meal (besides the excitement of street food is probably more fun for a kid than telling them to sit still for an hour while there is so much going on outside)
Because of the disproportionate cost of the plane tickets, if you were to stay longer than a week the cost compared to Disney gets increasingly better. There are also many other international locations that can be cheaper, and thousands of places just in the US filled with unique experiences and culture that can be engaging for kids at an even better price tag
If you can afford Disney go for it. But going into debt over it is like taking a payday loan to hit up a Cheesecake Factory when there's a block full of food trucks with a dozen cuisines just down the road for cheaper