To put it plainly, bayonets did not actually make sense until one could get saturation fire; not good but infrequent shooting like with a 17th c. arquebousse, but mass shooting that would overwhelm the lighter cavalry of the day (remember, the reitar killed the lancer by then!). The bayonet as a tool of last resort would make sense then, and help minimize casualties by gunfire by getting right into the fighting. Otherwise the bayonet was a really really poor pike substitute - behold the Swedes employing pike effectively against their bayonet-wielding opponents, and behold the rainy campaign on 1813 where even light cavalry on occasion hacked apart formed squares with bayonets (remember how badly the odds are stacked against the horse), because the rain turned the muskets into simple spears.
I would be very surprised if, say, Cossacks could break a pike square, yet they managed to chop through Napoleon's Young Guard.