I think the reason why most bicycles from the 1890s, that by today's standards would be called "Tall Frame" bicycles, is because at that time, that was the standard. We would call them tall frame nowadays, but back then there were not hardly any men's bikes that set any lower- other than the few boys bikes they had in those days. I reckon this is because frames that set down lower, had not yet really been developed, and would not remain so for another decade. And plus, people back them were used to having to get a running start to hop on a bicycle, as the only machines available prior to this were high-wheelers and the like, in which you have no choice but to get a running start. Even the women's bikes I've seen from those days are just as tall as the men's, and with women being, in general, a little shorter, they definitely had more trouble. Like you mentioned, average man in that time was 5ft and some change, with women being shorter. So in conclusion, I reckon it is for the same reason a 1910s-20s car is taller than a 50s or newer car; that is just the position the technology and development had reached at that time. Just about every 1890s bicycle I have seen sets up pretty tall, some a little more than others.
I could be totally wrong though; this is just what I believe to be the case from what I have seen, I am no expert.