I found it to be pretty clear sailing most of the time from Springfield to Albuquerque. Much of the old route is replaced with modern highway so although you're following the old Rt 66 pathway you're doing it on modern roads. The slowest portion would probably be in Missouri and Illinois because of towns. In many sections, mostly Oklahoma of what I rode, the old road is next to the current highway and is interrupted by missing bridges, crossings by the current road, etc. If one is primarily interested in following the old route and seeing the scenery along the old route there is no real advantage to actually putting your tires on it much of the time. In fact it would really slow you down as you would have to backtrack when you come to a missing section, then travel the current highway, then get back on the old road, and so on. If you wanted to run your tires on the old road surface as much as possible you probably would add as much as 50% to the travel time. In Oklahoma I did ride many miles on the old surface as it is concrete and still in decent condition. On those sections there was very little traffic so speed was normal.
I missed riding the section from Chandler, OK to Oklahoma City because of tornadoes. They were going to be tracking right up Rt 66 so I dropped south to I-40 and Shawnee, stayed there for the night, and watched on TV as the tornadoes tore up OK City!