Wow - in my position (US based consultant) we are the ones who have to take 11 PM - 1 AM status calls twice a week. We're the ones who have no accomodation from the Indian side because everyone needs to leave precisely at 5:33 PM IST to catch their bus to go home. We're the ones who have to lead changes during maintenance windows (overnight) because there are no suitable offshore counterparts who can execute on a playbook.
In a separate comment I mentioned that the rockstars offshore quickly move on, so when we do find a great resource they're often not around for long, leaving us to dip back in the pool of talent. If India is going to accept its new worldwide role of being the frontline tech sector frontrunner, it should probably start moving away from the "assimilation" type of education it's traditionally been doing and move more towards a more western "application of concepts" approach that you mentioned. There should be no reason at all someone, whether they be an onshore new hire or an offshore new hire, in a tech role at a really large IT company, should stop everything they're doing when confronted with a "Click Finish to Complete Installation" dialog box with an "OK" and "Cancel" button on it just because it wasn't detailed in the install doc. Click OK! Spread those wings and fly, baby bird! Learn on your own!
Maybe I'm the weird one who would like it more if someone said "I tried X, Y, and Z. They didn't work. Ideas?" as opposed to "I ran into this at 12 PM my time, tried nothing, and now it's 18 hours later and you have finally told me to click OK. Until I run into another dialog box that says "You sure?" with another OK button and we waste a complete day back and forth again."