There was basically no rich middle class which had the time and money to fool around with individual transportation, and the other classes had either no real reason to want this or it was pure luxury.

I also would think such people existed elsewhere in the world centuries ago.

Chinese wheelbarrows are the real endpoint of pre-industrial transportation.

Pretty much all modern rideshare bicycles do not have pneumatic tires, FWIW. Ride quality suffers, but it's not an awful tradeoff for short trips with whatever squishy compound they use now.

Carriages used to have suspensions (made from some elastic whale bone I believe).

If someone would attempt to build a bicycle in a time of carriages with carriage wheels, I would then expect this person to also copy (at least in analogy) the suspension systems for carriages of that time, if not on the first try at least on the second...

It's just some of the cheap dockless purveyors that use non-pneumatic tires, and these companies have been dropping like flies. The docked bikeshares by contrast are still (slowly) expanding with their superior, but admittedly more expensive, bicycles.

Anyone with the means to pay would much rather use an animal-pulled cart instead of literally making an ass of himself.

Or just ride a horse like a gentleman. (Until the 'mad dogs and Englishmen' craze hit.)