For one thing, Erie County is one of the bigger counties in NYS, being about 40+ miles long and from about 20 to 30 miles wide, so it's going to have lots of county roads.
I think the reason that the county has so many roads is that county "leaders" back years ago (1920s, I think) decided that having good roads (ie, paved) between villages (or hamlets) was important and that the only way that was going to happen was to have the county rather than the towns take care of it. This made sense in 1920 when most of Erie County was rural and farming was the main rural occupation, particularly dairy farming (which requires daily pick up of milk!).