Generally taxmen and cientists are useful for special purposes only and you should not have them in early expansion phase (pop a setteler instead).
The math bihind....
Each taxman/scientist gives 1 gold each turn to treas/science, and do require 2 food to survive. Imagine a 2 food -> 1 gold conversion.
Each field worker can add at least 1 g (tile w. road) to city income. This is multiplied by city improwments, and money to crruption is then reduced.
Basically there is no point keeping a worker collecting taxes when working a riverside he make 2 gpt (or 3 with marketplace).
101 reasons to use specialists:
1. (the most obvious) there are no more free tiles
2. corruption, if You're unable to get more than 1 g from a distant city, You migth be happy with few extra gold from taxmen.
3. 40 turn science with 1 scientist
4. Starving a captured city with all taxmen (my favorite form of ethnic cleansing)
5. balancing for WLKD (You do not allways need a entertainer) to have no one unhappy and lower corruption
6. to complete research while having revolution
7. to decrease city growth
8. to get better score
...and there must be dosens of more even though I cannot think of any other.
Finally I'd like to commen the entertainer issue by col and darkness:
note that the lux slder (on Domestic advisor screen) works best for core cities, which have low corruption. On far away cities increasinf lux rate does not help hence the corruption. my rule of thumb is to set the lux according to core cities near capital and use entertainers farther away when needed.
karl (student in civeconomics)