This is what the choice comes down to. Are India prepared to pick four out of eleven players primarily for their bowling outside Asia? In Asia, and especially in India, the choice has been simple. Ravichandran Ashwin, Ravindra Jadeja and Kuldeep Yadav have been world class spin bowling options. Axar Patel has typically been picked as the fifth bowler. Kuldeep Yadav is a tailender. But outside Asia, things change. For one thing, Ravindra Jadeja can play, at best, as a fifth bowler unless India find the rare pitch which affords two spinners. Such pitches have been available occasionally.
But when they have not been available, India have, in the recent past, been prepared to play four tailenders. A tailender is a player picked primarily to take wickets. Whether or not such a player is picked depends on whether they are picking wickets.
Hardik Pandya and Nitish Kumar Reddy are both all-rounders. Shardul Thakur is not. He was picked for his bowling and left out in favor of Prasidh Krishna when his bowling fell away.
India played 4 quicks in 14 Tests outside Asia in the 2018-22 period. They won 6 and lost 7 of these 14 Tests.
India played 3 quicks in 18 Tests outside Asia in the 2018-22 period (excl. Tests in West Indies, for a like-for-like comparison with the above). They won 5 and lost 10 of these 18 Tests.
Being prepared to play four tailenders outside Asia (or more precisely, in South Africa, England, New Zealand or Australia), has brought India better results. Playing the 4th bowler, at least in part for batting, has worked less well.
These stats should also have been available to the Indian team management as well.
Why do you think they still tilt the balance towards batting?
All senior players in the side today (Rohit, Bumrah, Jadeja, Kohli) have all been part of these test matches. These guys are not stupid enough to not know the merit in this argument.