The only other way to get wheels to turn is either roll them freely unbound to anything, or attach them to a rotor. You can adjust the suspension settings to make them ridged, and you can use vertically oriented suspensions to prevent side wobble as if it was on rails.
It's unclear at this point whether you'd lose any forward motion energy due to torque flex, but that can be tuned out of the system if required in any case. It's also unclear how much a pair of wheelchair-sized ASWs would cost at this point. We assume they're not cheap compared to a regular rim and tire setup. Here's some annoyingly infomercial-style video comparing regular wheelchair wheels to an ASW setup over curbs and grassy, uneven terrain.

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A heads up to politicians and city planners: stop wasting your money on bike lanes, tax incentives, and PSA campaigns. All you need do to persuade your constituents to trade in cars for bicycles on their morning commute...