If you have a pneumatic tire, the entire air volume of the tire is your first shock absorber; even before you have to care about suspension design, you're chopping out high frequency chatter and broadband impacts.

If you have a solid tire, only the arc between the axle and your contact patch is the shock absorber, and the rest of the tire remains relatively unperturbed and unable to contribute to smoothing out the road.

This results in a harsh ride.

Often, to get a tire compound to be sufficiently durable to work well in a solid tire, you have to sacrifice the ability to maintain grip over a reasonable operating temperature and road conditions. This also contributes to reduction of ride quality, and makes operating in wet or freezing temperatures potentially quite sketchy.