It's a pretty well-known fact in Indian universities than anyone even a teeny bit serious about computers should never step foot in consulting companies (unless you are leading a green field project).

Well that’s got to be impossible because how else do you guys get all the off shore work, if not through these companies?

Firstly, India has a huge engineering population. Even if 10% of it is interested in consulting jobs, it's easily more than most countries. Secondly, most folks do engineering just because it's easy path to get a decent paying job. They don't really care about engineering itself, so consulting jobs are a happy medium, also they provide easy transition to customer facing roles or management which many folks want to move to anyway.

And lastly, there's dearth of product based companies in India, so positions in such companies are highly lucrative and competitive. Consulting job is the last resort for someone interested in software.

This entire phenomenon is so common there's a popular comedy sketch on it - https://www.youtube.com/watch?v=oPp4htuqDOs Not really far from reality

If the institution implicitly understands its own incompetence (that they will explain away as "we just can't find good developers"), they know they can't win repeat contracts, so they optimize for milking the few that they do get.