The phrase "has been 'around' for a while" just means that something has existed, has been known or has been available for some time. It's more the previous sentence which suggests popularity - if the approach has been widespread in modern companies since the early 20th century, you could infer that it's been popular for this time.

It means his principles to improve efficiency are still being utilized today so yes, you could say his methods and principles are popular. “Been around for a while” simply means that something has been popular, used, talked about etc.. for a long duration of time, maybe days, maybe weeks, or even years depending on the context. Check out my teacher profile and schedule a professional English session. www.italki.com/teacherhelpme Thanks :-)

"Familiar" is probably a better word than popular.