Look at modern, traditional pastoralist cultures. Most rely on dairy for staple protein. Very few animals are kept for meat alone, in a traditional economic context. Most require several uses (plowing, transport, textiles, dairy, meat, currency) to justify their care.

Some cultures even outlaw eating beef, and most slaughter mostly when they don't have enough feed or for special occasions.

Dairy is absolutely essential to the nutritional economy of most pastoralist cultures that we know about. As you say, lactose persistence is not an absolute barrier... but I think this sort of evidence suggests that dairy is a very significant part of human history. Pastoralism with or without milk is a different beast.