I doubt whether it is possible to get real numbers on the number of bands, since they form and break with alarming frequency (usually because of something the drummer or his girlfriend did ;-).
But, speaking broadly, I think we can fairly say that being in a Rock/Pop band is a leisure activity, which is a fairly modern concept. Quoting from here, "The modern distinction between the ideas of work and leisure, like the regular alternation of work and leisure, was a product of industrial capitalism. Pre-industrial societies had festivals (together with informal and irregular breaks from work), while industrial societies have leisure, weekends and vacations."
After WWII, economies in industrialized nations have consistently achieved greater levels of productivity, creating more wealth with less work. Automation has decreased the percentage of non-work time that is required for daily living chores. This has given rise to a continual increase in leisure time. It is likely, therefore, that all leisure activities, including being in a Rock/Pop band, have also increased.
So, although I doubt if we can put absolute numbers to it, yes, it is likely that there are more bands today than ever before.