I'd be interested to see that. While yes people falling from a horse might be in trouble - generally horse will try to avoid danger themselves - and there would have been only so fast that you could ride a horse in a city, due to the roads available for this.
Generally, "cities" were much smaller (and fewer) then; not large enough to have much need to ride "through" one. Most horse-riding (though not carriaging) would involve using a horse to travel between the various towns in an area, via not-necessarily-well-kept roads.
Some non-negligible percentage of horse-riding was also done by the nobility, where the horses were used either for hunting, or for military campaigning—both places where a horse "avoiding danger" can actually be fatal.
Re: hunting, horses would often rear back from predatory-looking animals, dropping their riders and possibly dropping onto their riders, crushing and laming/killing them. "Hunting accident" was the old world's "boating accident."
Re: military cavalry usage, horses could be spooked into stampeding—this was an incredibly large problem when in a closely-packed cavalry formation. Cavalry warfare was phased out upon the introduction of guns not because horses were more likely to die by a bullet than by an arrowhead; but rather because the sound of rifle or cannonfire was usually enough to spook horses un-used to the sound, turning many of the first rifle-era battles into instant routs.
