I first heard of Rajamouli with Bahubali and then RRR, so my knowledge is limited, but I'll base my answer on these 3 movies.
For me, none of the movies were that amazing. They were both overrated. But they were definitely a good one time watch. Rajamouli did have some good characters in Ram and Bheem and he could have made the films slightly more realistic, but that complaint of mine is for another day.
Back to your topic.
I think he rose so much because his movies work anywhere. They are Telugu movies (I think), but really work in every language. They are larger than life with the typical masala makings, but the dubbing is adapted to get the same meaning across and to work on each scene.
Let's just look at Naatu Naatu as an example. The lyrics work in Telugu, Hindi, and probably any other language. And it isn't just a word-for-word translation. The lyrics are taken and repurposed into Hindi to present the same feelings.
Now the reason these movies work on a global scale is because they show the world a new presentation of Indian movies. They present the new age where we've moved past dancing around trees, landing up in Switzerland in skimpy sarees, and where the female is all pious. It presents this aggressive alpha who is untouchable, females who are strong, and dance moves that put Michael Jackson to shame (like how he made moonwalk famous).
His movies work with the global audience because those are the types of movies that many of them like nowadays. After COVID (and even before it), the movies that did well in theatres were those that were about superheroes. Pick up any Marvel movie. Most likely it was a super success (barring a few). RRR and Bahubali were on that level with their alpha males not story lines (untouchable, lots of action, basically like a superhero).
RRR and Naatu Naatu did so well on a global scale also because of the actors I feel. When Rajamouli started pushing for RRR to go the Golden Globes and then the Oscars, we saw 2 actors who were down-to-earth, love their country, and just want their film and Indian cinema to be recognized on a global scale. People loved these 2 actors as well. I mean just look at wherever Ram Charan went. Everyone from Indians to the most gore of folks were screaming his name and he's folding his hands in respect, taking selfies with people with a smile, and then waving his way past them. Ram Charan and Jr NTR wore Indian attire to the Oscars and celebrated in the sweetest way possible. Somewhere they were able to bring Rajamouli even more success.
Now this is just my theory, but I feel like I can put all these together to explain why he's a global success today.
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