With programming the information is always there. If you don't understand a higher level language but do understand the language in which the compiler is implemented, you can always read the compiler.
The "it trivially follows", the information is simply missing. Gaining a mathematics degree will often give you the intellectual power of finding the missing pieces yourself, but the only sure way is to ask the authors themselves.
Getting a math degree just to be able to fill in the gaps created where 'it trivially follows' is equivalent to being required to memorize the API for a framework because clearly defined documentation is hidden behind a paywall.
so called 'intellectual power' has little to do with it. What you're describing is familiarity with navigating a minefield of poorly structured information and tapping a academia (ie at a very high cost of entry) for 'special access' to resources that bridge the gaps.
Of software development suffered from the same informational constraints and lack of innovation, we'd still be playing pong.
Hmm you are from US aren't you? :)
To be cynical about it.
I guess that's not much different from most fields' use of specialized vocabulary, etc. There are many informal methods of dissuading people from competing in your own little corner of the labor market.