As far as I see it India have one big advantage, which is that their first class system with its lengthy season is still intact. Australia's and especially England's have been suborned to limited overs crap and SA has the problem of better batsmen like Roussow departing. For whatever the technical faults their players may have the Indian system does have one thing, which is that batsmen can learn to pile up massive scores with regularity. In comparison in Eng or Aus you have batsmen being selected for tests who average mid-high thirties and score four fifties for each century. This is the result of the 'natural game', limited overs, 'positive' mindset in Aus and playing in sub-optimal, shoulder season conditions in Eng. Yes you have plenty of limited-overs type, ill-disciplined Indian batsmen, and the IPL is the big thing in town, but Aus at the moment could never produce an Agarwal. We simply don't reward batsmen who score slowly or bloom late, there's too much focus on white ball u19 etc. so young players don't play grade against much more experienced players, and any batsman who gets in the international setup plays very little fc cricket even in comparison to Eng players due to white ball internationals. The quality of Indian FC cricket is lower than in Aus, Eng or SA, but it can still produce batsmen who have discipline and know how to get a big score. For whatever reason, either the ones I just explained or something else, the other countries can't.
With respect to conditions, I think there's a few factors. Firstly, in Eng, the poor scheduling means batting in damp conditions that favour neither spin nor express pace, but are hard to survive in, so batsmen never learn how to score, and genuinely fast and spin bowlers never get matches let alone learn how to bowl. In SA and Aus the pitches are better for scoring (but offset in Aus by the disdain of batting discipline) but there seems to be little variety. I can't comment too much on SA but in Aus the Shield pitches either seem to be flatish or greenish. There's hardly ever a genuinely fast, turning or inconsistent pitch. In all three of SA, Eng and Aus this is pronounced with respect to spinning pitches, hence the trouble with both playing spin and producing spinners. India probably doesn't have that great a variety, all their batsmen except Kohli were exposed by swing and seam in England in 2018, and their spin bowlers hardly set the world alight outside of Asia. But they are nigh unbeatable at home, and because they know how to score will stand a better chance in countries that produce flatter pitches like Australia than Aus or Eng would in India. I don't know that India's players are more rounded now compared to say, the mid 00's (except for having good pace bowling) but those from SA, Eng and Aus have become demonstrably less rounded, and it's making the conditions gap in Asia bigger and outside smaller. I think there's also the tactics which touring teams adopt in India especially wrt pace bowling, but I've prattled more than enough.