With that many kids, we are PG with our 4th so I am with you, I would suggest a larger SUV, such as a Suburban, or Yukon XL (same thing). With the smaller SUVs for crossovers, you will have little cargo space and with 4 kids, you need room for stuff. You don't want to end up creating many projectiles, but piling things in the seats near your kids because your cargo space is full.
I have a Yukon XL and I LOVE it! Sadly with 2 large seats in the 3rd row, Frontier in booster mode and Regent, you cannot have another passenger or seat back there, that row is full. I have a bench seat in my middle row, I LOVE this. DD is currently RF in a Marathon in the middle seat of this row. It still leaves the drivers side seat of that middle row open. Then I fold down the passenger side portion, this seat is a 40/60 split, for my boys to access the 3rd row. If we need that extra seat, which we will when we have guests, once the baby arrives and we fill that drivers side middle row seat, then we can fold up that 40 seat after the boys are loaded.
I see lots of families loading kids through rear doors of SUV/Crossovers at school pick up. So this isn't uncommon, but could be a real PITA if you had your cargo area full.
Good luck deciding. I am certainly glad we already have a vehicle big enough to haul all of us. Not something I would want to have to deal with when PG.