Even navigating stairs with a dolly is easier than carrying a heavy weight, and much safer, too.
I'm utterly unconvinced by Jared Diamond's claim that lack of pack animals made the wheel irrelevant.
Oh, and any significant construction site would find it useful to make a road to it, even if they only were carrying things.
Even when barging heavy loads, to get the load off the barge and up to the site a dolly is still highly useful.
In any case, the baggage cart like you're describing, or maybe a hand truck, seem to be both artifacts coming out of industrialized society. I'm not sure how useful one would be on a steep hill if the cart itself, including the axle and wheels, were made of wood. You don't really see modern, usable baggage carts until the industrialized production of steel (I'd love to be corrected). Hand carts? Sure, but of a more significant weight:load ratio meant for longer distance, heavy load, flat hauling—remember these suckers often have brakes you wouldn't want to engage on a runaway cart, like a peg through the spoke or axle or a wedge under the wheels.
I'd think some kind of carrying + strap frame like you see today would be a better fit for personal hauling and balsa might even work well for it.
https://en.wikipedia.org/wiki/Ljubljana_Marshes_Wheel
Wheel & axle made of wood, for a two wheel push cart.
Spend some time using an ordinary dolly to move heavy boxes around, then try carrying them. There's just no comparison.
Besides, it's one thing to say that wheel technology is gated by metals technology, quite another to say it is gated by the existence of pack animals.
I’m pointing out projecting modern needs backwards out of speculation isn’t likely to yield much understanding of why someone didn’t invent a handcart in precolumbian mesoamerica. Jared Diamond at least compares the material conditions of the two sets of continents—that seems like a decent tactic for approaching the past, even if I do have large complaints with his confident narratives.
I've been to Chichen-Inza. It's flat.
The Egyptian chariots had wooden wheels and axles, and were light.
https://www.brown.edu/Departments/Joukowsky_Institute/course...
The axle is also very clearly a turned part, probably made on a lathe.
A rail road even. Dogs and goats are useful for pulling sleds over a rail. Or a trail.
I agree that the size of the animal doesn't makes wheels less worthwhile.
They aren't super-great in hilly terrain, though.