Yeah, the Arduino is 8 bit, but how often do you need to compute this? I geeked out and looked at the Steinhart-Hart Equation. Looks like computing (ln) is the worst of it and you only need to do that once in that equation.
It could be inconveniently slow, but even on the Uno, the docs I found on the Internet suggest around 30,000 float divides/sec. Multiplies are 3 times as fast. So, it might take a millisecond or two on an Arduino.
On other older microcontrollers, it'd be a lot slower though.
Thanks to OP for giving this PhD in CS something fun to research for the evening.
There is a forum member called crane who has done all these calculations and verified the accuracy of simple thermistors over a useful range using the coefficients published in the datasheet.
I agree that for brewing we don't need the calculations to be all that fast so the look up table is overkill. It's nice to know how it is done though.
Cost is not a huge issue but there may be applications where thermistors are more useful or convenient. For example if you want to measure temperature by sticking a probe to the outside of a pipe I would use a thermistor because you can get thin ones that lie flat.