Did a daily commute through York for about 15 years from 1992. Mostly ok with the occasional incident, t-boned by a camper van, for example. The worst bit were parents dropping off kids at St Peters public school. So many SUVs, all in too much of a hurry to worry about plebs on bicycles!
The cycle track is ok, apart from hordes of dog-walkers some of whom are irresponsible, but cycling around the retail parks is very tricky: Clifton Moor, Monks Cross. Luckily my employer never moved me their Monks Cross office as I would not have enjoyed cycling there.
Another major problem for cyclists is that cars just get bigger and bigger, taking up more and more road-space. York does not have space for wider roads and who in their right mind wants to give over more of the city to cars, anyway.