But efficient enough to go some distance, reliable enough not to need a full-time repair-man, and cheap enough to be sold to people who didn't already own a horse & carriage? That needed lots more technology.
You also need people to ride it. It wouldn't fly as a palace amusement because the king (and more importantly the little prince) would keep falling off. They won't have an incentive to value the skill until there is a horde of middle-class, 19th century, hipsters showing him up.
A circus act is more plausible, but only if there's some continuum of other simpler circus equipment leading up to this rather sophisticated bit of engineering.
I suspect you could make a perfectly acceptable modern bicycle with 18th century technology, albeit not as durable. Metal axles aren't much of a problem. Light and strong wheels are trickier, but you could get away with solid wooden ones, or emulate modern spoke systems with sturdy leather strands. The chain is difficult point - leather won't cut it as you need immense tensile strength and rigidity - but if you didn't want to meticulously hand-craft a modern chain (possible but tedious), a direct-gear solution might be practically possible.
No, what was missing was the very concept that it would be a worthwhile thing to attempt to build. It would have taken an incredible visionary to follow the above steps, especially in a world where the poor quality of roads made such a device of questionable value. And anyone rich enough to afford such a thing was doubtless rich enough to afford a horse carriage - who in that set would aspire to pedal through the mud?
tl;dr expensive, flimsy bicycles are completely useless in a world with poor roads and deep wealth inequality.
You make a last great point with this.
Without paved roads, rubber, decent springs; all of the shortcomings are amplified. The gear drive works, but if you have a wood wheel, with a wood axle, w/ wood cogs, the tolerances to be both comfortable and effective on cobblestone or dirt would be troublesome.
as a one-word piece of supporting evidence, let me just say - Boneshakers.
[1] https://www.britannica.com/technology/vulcanization [2] https://www.britannica.com/technology/tire#ref117797
Leonardo da Vinci could have built a Chukudu in 1490.
https://electrek.co/2019/05/23/first-ride-rungu-three-wheele...
Leather is good enough for motorcycle drive belts. Nowadays belt drive bikes use cogged composite belts, but once upon a time they were leather.
Bearings could have been polished and oiled wood. The frame, wood. The hinge of the front wheel, brass or another small bit of steel. Transmission could be a leather belt. Wheels, wood again.
Would such a device somehow emulate a modern bicycle? Very likely.
Would such a device be practical, reliable, fast, to say nothing of comfort? I greatly doubt it.