Why are median transaction fees so much higher now (in october 2017) than a year ago?
The relation between average transaction size and average transaction fee is not linear. 


  Are people still falling for bad fee prediction algorithms?


There are no good prediction algorithms here. Think about 110 people waiting for  a bus, but the bus has only 100 seats. 


  Is there an increased demand for quickly-confirming transactions?


I don't think so. Most of users do not care at all about transaction fees while their capital grows.