I am not to well versed in other “folk” religions but I do agree Shinto is one that is very prominent in Japanese culture and societal practices. However I do have to clarify that Shinto is not “folk” in that it is not wholly indigenous. Buddhism and Chinese influences have left deep impacts on how Shinto has formed over time. But back to your main question.

I’d say the main reason as to why Shinto is practiced as widely as it is today is because of the retooling it went under during the Meiji restoration. During the Meiji restoration Shinto was a state-backed institution and adopted many of the traits we see today. To emphasize the state nature of it, even Shinto priests were selected by the government and the Shrines were used as registers for people of the local community. So the main reason Shinto is still prevalent is the large government retooling and intervention that occurred during the Meiji restoration. In addition, during the early 1900s Shinto was being taught in schools and the entirety of the nation was united under the Emperor. The Emperors power stemmed from the idea that he was the Descendant of the Sun-Goddess Amaterasu. As you can see, the government and Shintoism were heavily intertwined.

To try to put it simply, it is so prevalent today because it became a government backed institution during the late 1800s up until the end of WW2. I do not know of many other folk religions that have been so heavily pushed by the government onto the people.