As most cars age they tend to get "looser", which is caused by hardening of bushings, tire wear, and general wear and tear. This degradation in ride quality is so slow that it often goes unnoticed until a drive over a stretch of road you haven't traversed for a while sets off a light bulb. Sometimes it's primarily the tires.
A fresh set of tires with a full depth of new resilient rubber will provide attenuation to high frequency road inputs than the thin layer of hardened rubber on a worn tire won't, however, shorter/stiffer sidewall replacement tires will almost always generate more ride harshness than the higher OEM profile. OEMs tune the NVH characteristics to the OEM tires, and significant deviations from the OEM tires will often yield a significantly worse NVH profile.