I agree with you in essence but there are a lot of differences between USA and India in this context. Prep and tuition fees are inhibiting for most of the potential aspirants but they are much lower than in the US. The result is that way way more people are able to prepare for and take these entrance exams. In the US on the other hand, you first need an ultra expensive undergrad degree, then medical school applications and interviews and so forth. In India, massive tutoring companies are the beneficiaries. Allen Career Institute for example posted a total revenue of about INR 20,000,000,000 last year and there are four or five other companies like this along with the god knows many small businesses and individuals in this sector. All this for preparing high school students for entrance exams. There is a city called Kota in Rajasthan where:

Over 150,000 students from all over the country flock every year towards the city for preparation of various exams such as IIT-JEE and NEET-UG etc.

(Hostels in Kota are outfitted with special ceiling fans designed to prevent suicide by hanging.)

Those who are very wealthy and want to skip this process do one of two things. They either study abroad. Or study in private colleges where admissions can be bought but they are usually not considered prestigious, not that it matters to those already with a lot of wealth. There is little advantage that an extremely wealthy aspirant has in these exams compared to someone who is moderately wealthy or even just upper middle class.

These exams are rather meant as a bottleneck between an extremely large number of aspirants and an extremely low number of vacancies in higher education. The exams are very difficult to present an illusion of meritocracy but the "competitiveness" is a foil for a weak and wanting education system.

The system you suggest would work in a better society but the whole political economy does the opposite of what it claims to do and what people think it should do.

Like the doctor shortage you mention is very real and severe. But there is no immediate financial incentive in fulfilling it. The ruling class hates public health in general. So the (official) life expectancy is sitting at a cool 68 while potential doctors pursue medicine for money rather than any nobler notions and people blame minority groups for producing "bad" doctors because of affirmative action.

The cause of the shortage has nothing to do with the pre degree required. It is entirely the limited space in medschools and the arbitrary lottery system of the accrediting body, which is corrupt.

The point of half the classes in undergrad is to allow those doctors to branch out and not just be single minded careerists. Those classes are supposed to make them think, experience new viewpoints, broaden their perspectives, and develop them as people. Not taking those classes has the same reasoning as the compsci and engineer students who whine and moan about being forced to take ethics or humanities courses.

Also taking basic biology, anatomy, and chemistry as part of medschool would be extremely inefficient, and the predegree builds a basic level of knowledge that doctors should have going into medschool.

Also of a person stops wanting to be a doctor in undergrad, they can easily switch over, as opposed to your trade school idea which would lock them into a single grouping of career paths unless they drop out.

I agree current systems disproportionally favour wealth over merit but given limited resources how would one filter candidates efficiently to select those truly motivated and disciplined to study? If one approaches the problem by eliminating privatisation of education you can then work towards a more meritocratic system with or without entrance exams?

I suspect the number of Indian immigrant doctors abroad is due to brain drain rather than an abundance of doctors/lack of need in India.

He wrote about this in 91 from what I know. Don't know of other instances of him talking about this:

Comparing India's death rate of 12 per thousand with China's of 7 per thousand, and applying that difference to the Indian population of 781 million in 1986, we get an estimate of excess normal mortality in India of 3.9 million per year. This implies that every eight years or so more people die in India because of its higher regular death rate than died in China in the gigantic famine of 1958–61.3

https://academic.oup.com/book/2070/chapter/141991095