Actually there's a very easy empirical way to test this claim: look at the amount of subsampling pollsters do. In the US samples are typically weighted after the raw data is collected, by:
gender
age
white college, white non-college, Black, Latino/Hispanic, Asian
party registration
For 1000 samples you get the standard MoE of 3ish percent.
In India you start by dividing up the electorate into hundreds of strata, sample independently from each stratum, then piece it together. This results in Indian polling sample sizes being over 100k for the same 3% MoE.
This is pretty objective evidence of India's diversity.
(I am curious though if 2024 is going to cause pollsters to re-examine polling basics in the US. There are several major warning signs this year that polling is broken, even if it produces the right result in the end.)