For a stroller, yeah it would be tough to load one on top of a set of drawers. TBH, the only stroller I used with any frequency was a small folding one when the kids were <6 months (my wife used it a bit more, though)I have the Yakima drawers stashed in the shed at the moment. With a stroller and other baby-related stuff I found them to be slightly prohibitive. They're great for wheeling but just didn't work for me on an everyday basis; YMMV.
After that, I'd put one of them in the Deuter kid backpack, which they both used up to about 40 pounds. Including in the woods and walking around the city. I honestly hated using the stroller, but loved hauling kids in the backpack. It was a sad day when they were both too big for it.