For convenience, aside from sliding doors, a minivan like the Odyssey also offers more LATCH and tethers than most SUVs. Our Highlander is pretty sad in that regard. Not sure about the latest Sequoia, though. Also, the third row of most minivans folds out of the cargo space, leaving a nice, deep well behind it when it is in use. That's very handy for cargo when you have a full load of 7 or 8 passengers and is one of the things I miss in my SUV.
Minivans like Odyssey and Sienna offer a lot more space than midsize SUVs and even a little bigger than some full size models like Sequoia. For example, Honda lists cargo volume as 148.5 cu ft behind the first row, 93.1 behind the second row and 38.4 behind the 3rd row vs. Toyota's numbers for the Sequoia are 120.1, 66.6 and 18.9, respetively.
I know price, fuel economy and crash tests aren't the most important buying factors to everyone, but Odyssey really comes out ahead compared to just about any full size SUV in those areas. Comparing the Touring Elite to the 2WD Platinum, the Sequoia is close to 33% higher in cost (60k vs. 45k MSRP), while the Odyssey gets almost 50% better fuel economy (22mpg overall vs 15mpg overall). That's a real difference when you don't appear to get any more space, maybe even less. Most full size SUVs have minimal crash test information to compare to the Odyssey's top results.
I was pretty much looking for any way to be done with a minivan and I really like driving my midsize Highlander Hybrid, but it's definitely a step down in space and seating. Of course, you don't lose as much utility if you go to a full size SUV, as long as you don't mind the higher price tag and worse fuel economy. And, as I said before, if you really do need heavy-duty towing or off-roading capability, you'd want the truck based SUV.
Lots of people put 4 kids in a full size sedan and aren't any worse for it
If you can afford the cost of a new Odyssey or Sequoia, you'll likely be very happy and fortunate with either one!