It’s not “moving to India” so much as Western studios are now forming smaller core teams locally and farming out much of the content to outsourcing studios in India, Malaysia & Eastern Europe rather than doing it all in-house.
As someone in the industry, I have not seen this across studios.
If you farm out art, you end up with a confused set of props / designs. If you farm out code, you end up with a mess of different assumptions and patterns.
If you’re designing and considering everything, then you’re essentially running a studio but now remotely from another country.
I don’t disagree with the problems you mention, but US and European wages are high, and margins keep getting tighter and tighter.
A lead studio with a small headcount can outsource work internationally for often much cheaper than the same job done locally, but also not have to pay those workers in stages of development where there’s not enough work for them.
Typically game/media studios run on contractors because of this. You'll be hired for maybe 3-6 months on a repeating contract, so that you can be let go at a moments notice.
For businesses the labour entry point is crowded, wages therefore are low. We find it more common to hire students and pay minimally, use exposure as the negotiating tool.
I know multiple publishers who advocate for that model; outsourcing, not so much. Unless they have a trusted partner, but at that point, they're essentially acting as an arm of the publisher.