As you have pointed out correctly, there is excess of doctors in Indian 'cities', it is not unsual find 10 doc offices standing side by side on a given street. Like everything in India, this one end of extreme. There are whole 'mohallas' - precincts of hospitals in some cities. There' a huge chasm in number of doctor available per unit population in rural and urban India. The ratio is very much skewed in favour of the later.
As for MBA, US universities put lot of emphasis on students having a couple of years experience before they accept them to their programmes. This is something which usually doesn't really fit into linear relationship of completing one's education first and then getting a job so deeply engrained in mindsets of Indian student. This is sometimes necessary, because almost always parents are paying for education of their child eg., i'm 24 and graduated from medical college but i'm still living off my father's money. And, evem this picture is changing in India. Now that we have more and more banks offering cheap education loans, student's are becoming independent of parents in financing their education. Doing MBA with all its lucre is very much 'in thing' these days in India, even doctors are giving MBA a second thought. A recent report in a Mumbai newspaper reported 300% rise in application for CAT this year against 54% decline in MH-CET applications. It's not just that they are applying for CAT/SNAP/XAT but a lot of them are taking GMAT. I have littld doubt there as many if not greater number of people taking GMAT as there those taking USMLE here in India. Medicine as a doorway to upward mobility for Indian middle class is fast losing its appeal.
And as for, finding domestic help I would just like to say that manpower is dirt cheap here. There are no labour laws, no tribunals to redress exploitation for people employed in unorganised jobs such as domestic help. Life of poors in India is very cheap.
To live hassle free, good life in India needs lot of money. And, you can't earn lot of money in India without getting your hands dirty. That is why finding domestic help is least of worries for those willing to emigrate. Its rather a non issue for them.
I've been a bit incoherent putting down my thoughts but I hope you get geist of my argument.