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That's why I think the synergy between potters and cart makers is not enough discussed in histories looking at the wheel. You're laying down coils of clay to make pots: a freely turning work surface really helps make that easier, and doesn't require fancy engineering. You get impatient and spin the work surface, and discover that shaping the clay as it spins under your hands is a thing. From there, it's entirely worthwhile and feasible to iterate on that spinning work surface to make it spin more easily, more smoothly, with less effort, and able to spin faster. On the other hand, getting from a small miniature wheeled figurine to a cart that could hold a load and still roll easily was a much harder problem with a steep learning curve and not a lot of room for iterating from a crappy initial design to a working design.

So I think all the hard engineering in wheel invention happened among potters, and then only after they had the whole wheel-axle thing pretty much nailed did someone interested in making a better way to haul heavy loads come along and start working on taking a pair of potters wheels and using them to scale up those miniature wheeled figurines into a load bearing cart. It just so happened that the people who perfected potters wheels also happened to have draft animals they could hitch to that cart, which helped.