Yes. But those indians in favor of the caste system remain "backward" - it's not just something like poverty keeping the lower castes back and the rich getting an extra advantage over others to have their kids be rich.
It adds a further layer of pure discrimination akin to very heavy racism.
Imagine the poor considered not only poor, but inferior human beings -- and not allowed (or accepted by "civilized" upper caste people, when legal) to do many things even if they have the money to do them.
There are mechanisms (and we can discuss their effectiveness) that try to balance the playing field in provision of opportunity - but there's a huge gap in "provision to cope with failure"
e.g. Two people graduate with equal abilities and are offered an opportunity to found a start-up. One of those people knows his parents can cover rent/food if things don't go to plan, and the other will be homeless (or maybe more likely would have accumulate personal debt, or leave the city and move back to parents). One of those people is more likely to be able to take that risk and therefore more likely to reap a reward.
I'm not even sure I can think of a fair way to level this.
The only way is to reduce the pre-existing wealth inequality. Which is why a lot of people are in favour of strongly progressive taxation.
I don't actually think this is a better solution than progressive taxation and decent welfare though (and I'd also have no idea how you'd coax the market in that direction anyway), because it doesn't also solve the problem of the economy losing out on potential successful businesses because their owners weren't wealthy enough to start them.
You really think inequality is stablizing instead of compounding at the moment? Wealth ratios between highest and lowest have gone through the roof over the last 50 years.
"Oh look at those poor backward indians!!"
Well, most of the rich people I know had rich parents.
If you can live with your parents while building your company or they gift you a few thousand dollars, that's often the make or break factor that saves your ass when pivoting a few times.