The lower the profile (aspect ratio) of the tire, the rougher the ride.
As you increase the diameter of the wheel, the tire sidewall
dimension, and aspect ratio, must decrease. The tire's sidewall
functions as a spring, just as does your suspension.
Early radial tires had an aspect ratio of 80, a.k.a. 80-series tires -
a rather narrow treadwidth on a 15 inch tire, for example. The ride
was generally very good. As the ratio dropped to 78-series, 75-series,
70-series, 65-series, 60-series, 55-series, and so on, the sidewall
height continually became smaller. There is less sidewall to absorb
the road imperfections, and certainly pot holes, etc. Wheel damage is
much more likely with the newer designs with very low profile tires.
Tire sidewall technology has improved, but it doesn't change the fact
there is less "spring" available at the tire to absorb impact forces.
Yes, a GLS will provide a smoother ride than the LX. That said, you
probably could find a tire that will provide a better ride than the
stock tires on the LX. Your Mercury probably had either 15" or 16"
wheels with either 70-series or 60-series tires. And, the suspension
system is certainly more supple (by design) than the Sonata, plus the
wheelbase is longer, thereby providing a decent ride.
IMO, the move to larger wheel diameters has a practical limit. The
giant wheels seen on some cars today, i.e. 20" or 22", are not only
impractical for every day use, but look stupid on the cars on which
they've been installed.