True in Rajasthan and Madhya Pradesh as well (have lived there for years).

Between these four states alone, we're talking about 40% of the country's population.

If more than half of your country believes something, it can be said to be the majority opinion.

You wrote: <<Between these four states alone, we're talking about 40% of the country's population.>>

Google Sensei tells me:

    UP: 204.2M
    Bihar: 99.02M
    Rajasthan: 68.89M
    Madhya Pradesh: 73.34M

Not even close to 40%. Population of India is about 1.3B to 1.4B.

Those numbers are way too old. Even by the 2011 census, UP was nearly 200M with a decadal growth rate of 20% in the previous decade. Bihar was 104M with a 25% growth rate.

Even with more muted growth, current population would be 230M+ for UP and 125M+ for Bihar.

Not really.

IAS folk make on the order of a $1M/pa with all their kickbacks. They often even get to send their kids to study in the West for "free" through "scholarships" (as a quid-pro-quo for compromising national interest). The demand is quite high (see marriage portals).

IPS is one tier lower. Though, anyone who has studied the hallowed history of the former commission of Mumbai knows this is also not something to sneeze at.

Is that because of their geographical proximity to New Delhi, the capital?

No, it's because these states have fewer options.