How could it be less efficient than walking? Unless your region is perfectly flat, you could walk the bike uphill and ride downhill and still save ~50% of the effort of traveling any medium distance.

Only 50% if you count walking around carrying a table as 100% the same as just walking :)

That said, my non-expert opinion is that a penny-farthing without ball-bearings would probably still work OK; a rover-style bike with a chain would be much harder. But the ability to make bicycle chain, and the ability to make spokes for wheels, I think these happened about the same time too.