Anaerobic training is important especially for crits and I speak from my own experience as a cat 5 this year. In my first training race of the season, I was dropped quickly because I couldn't handle the constant accelerations. I had been spending the off-season building a solid LT base. While I could hold LT pace for hours, I couldn't handle the lactate buildup from anaerobic efforts and had to drop the pace way down to recover.
Now that I have several training races under my belt and the evening outdoor training rides have commenced I find myself becoming much more capable of handling anaerobic efforts and being able to recover from them at or near LT pace as opposed to endurance or recovery pace.