Why not use cowpox?

Okay, so the vaccination for small pox was discovred because of a related disease, called cow pox that was by and large harmless. Would it be a good idea to expose people to cowpox so they’ll get an immunity to small pox? Vaccinations take a long time to grow, but people could spread cowpox easily.

My WAG (and IANAD) is:

Though smallpox is much more deadly than cowpox, cowpox still carries some risk in children/elderly/the immune suppressed/etc…so they prefer the vaccine.

Not only that, but then you’d have to worry about cows getting it.

Also of interest (from here)

Vaccine’s much safer. Jenner originally made the connection because the milkmaids that were immune to smallpox had pustules on their hands from cowpox. Pustule is an ugly-sounding enough word that I shouldn’t need to explain further.

This from a guy named Smeghead?

I resemble that remark…