> Or in analog terms they'd just be a resistor whose value can be changed

For what it's worth, that's actually a thing (ReRAM/memristors), but I think it got put on the back burner because it requires novel materials and nobody figured out how to cost-effectively scale up the fabrication versus scaling up flash memory. I saw some mention recently that advances in perovskite materials (a big deal lately due to potential solar applications) might revive the concept.