there are still penny farthing races held today, mostly for fun/charity events, and yes people still fall off them constantly.
basically got replaced by the "safety bicycle" in the 1880s, equal sized wheels, chain drive, actual brakes. people were constantly faceplanting off the penny farthing's giant front wheel (it was even called "taking a header," that's where the phrase comes from lol). now it's just a novelty thing you see at old-timey cycling meets.
the giant front wheel size was actually a feature, not a flaw at first, bigger wheel meant more distance per pedal rotation, which is all they had before gears existed.