I think a Mazda five works great for 2 or 3 kids. You have the flexibility to move kids around as they age, and can haul an extra kid or two with no problem. But to have it consistently loaded with 4 kids plus 2 adults is not going to be comfortable. Obviously it is doable, just depends how often you need to fit everyone in the car, whether you plan to take trips with it, etc.
The common advice is to just rent a minivan if you want to take a long trip and need the room. Well, I looked into that and there were no Minoans available to rent at any price in my city. I could have rented a giant SUV for 100$ a day. So with four kids, yah, just buy a van.
The other complaint I have with Mazda fives is that their combined fuel economy is 24. An odyssey, sienna, or grand caravan will get you a combined 22, 21, and 20. City is 18 or 19 compared to 21, so even less difference. So you are losing a huge amount of space and flexibility for such a small improvement in fuel economy. Now, I haven't researched it in depth, maybe Mazda fives tend to do better than their stated fuel economy, and maybe vans are the opposite.
(Full disclosure, we shopped for vans and Mazda fives, couldn't make our minds up, so bought nothing, and were later gifted an old sienna, which I love with the passion of one thousand suns.)