I'm not a historian but as a physician, I can answer part of this question, and speculate about the prevalence of male pattern hair loss in other periods.

You're correct that balding (androgenetic alopecia) is less prevalent in Asian and African(-American) populations.

Androgenetic alopecia is less common in Asian and African-American men than Caucasians and also starts later in life in these populations. Estimates suggest that African-American men are four times less likely to develop androgenetic alopecia than Caucasian men. Approximately 30 percent of Caucasian men will develop androgenetic alopecia by age 30, 50 percent by age 50, and 80 percent by age 70. (Setty, 1972).

Balding is considered an androgen-dependent trait that requires a genetic predisposition. Men with a greater number of family members affected by male androgenetic alopecia are at an increased risk. Nutrition, trauma, and infections are also relevant factors to consider, but I don't think these are as important today as they were in, say, Roman times. Males castrated during puberty did not develop androgenetic alopecia, though I can only speculate that castration was probably more common in Roman times, and in East Asian empires.

In summary, I'd say yes, but the major reason for the increase in prevalence is due to the fact that more men are living longer.