Someone recently asked about airless tires so this is timely that the conversation comes back around to it. Like Pete, I used airless tires for a while, maybe 10 years. Eventually I found out that some of my courses, especially on rough surfaces, seemed to have been slightly short, a scary thought.
I switched to pneumatic tires and I gotta say the ride is a lot more comfortable! Also I feel more confident about riding on all kinds of surfaces: pneumatics, when calibrated on smooth surfaces, at least don't seem to lead to short courses.
Although as Mike has pointed out they can certainly lead to other problems!