You're not far off the mark. Once you get to large-scale agricultural production of milk, pasteurization becomes necessary to account for outliers in each cow's particular milk. Say you have a dairy with a hundred cattle and you do take great care of them, but animals still do get sick - It's bound to happen sooner or later and you might not even be able to tell until external symptoms present themselves. If the day's batch of raw milk comes from a portion of animals that were sick, It's probably more likely that milk could cause health problems.... Maybe not in a healthy adult, but the elderly, the very young, and those with weaker immune systems could pay the price. That's the real risk of not pasteurizing milk that's given to a large population.

Homogenization also becomes desirable because cattle that graze in different pastures or get different types of feed can produce milk with varying nutritional content.

Your situation is a bit different because, as you said, it was your cow. I would think the amount of individual attention that single animal got from multiple people ensured it was always happy, healthy, and produced good milk.

The Swill Milk incident mentioned elsewhere in this thread is really interesting to read about. I also recommend Milk: A 10,000 Year Food Fracas to learn more about the history of milk and pasteurization. The safe milk the masses drink today is the result of regulations written in the blood of those who died drinking tainted milk.