Cast iron wheels just don't have much traction on grass, and the as-cast (NOT machined smooth) gears in the old clunker we had lost most of the input in grinding and clashing and groaning lost motion.
Later vaguely similar models at least added brass/bronze bushings on the gear shafts; but the one I used was as-cast iron on steel rivets all the way through.
I think the "roller" on the back was replaced with an old pastry rolling pin 'cause the original (which might have been wood) had decayed before they dug it out at some archaeological site a century or two before I ever saw it - ca. 1945.
I think part of the situation related to "daddy" not being too keen on keeping a nicely trimmed lawn. We used to get instructions to "play in the tall grass" so we'd keep it tromped down. And generally we kept the front and side yards down to mostly bare dirt.