>"I intended to visit China in the near future -- but I've booked a trip to Taiwan instead, almost entirely because Taiwan doesn't require me to get a visa."
You still get a visa to enter Taiwan. It's just a "visa on arrival" as opposed to needing to obtain a visa prior to travel. Visa policies are reciprocal between countries. China and the US both charge citizens from each other's countries to visit for tourist purposes and that must be paid prior to travel. Tourist visa policies and immigrations polices have very little if anything to do with each other.
I think you might be short changing yourself if your only reason for not visiting mainland China is solely because they require a visa. It's less than a hundred bucks, it's basically a tourist tax. You likely won't regret it.