It makes sense that driving yourself is ok. IRL you'd be able to drive yourself to the hospital, and wouldn't want to wait on a taxi to arrive. Not to metion the angry taxi driver.
I'm wondering if Maxis knows about the stuck belly issue though. Not that they're likely to fix it if they do/did.

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Ok, oddly enough, I got the same results with the taxi that I did with the car. It allowed the sim to travel to community lots up until the last couple of hours before birth. I suspect there's a mod out there that's keeping people from being able to send pregnant sims to community lots.