And what about the principle of a mathematical proof having rigour? Jordi denounces the inscrutable tool used to create the proof but not the negligent mathematician who accepts the partial proof as valid!

And why would anyone pay for a software package and then "tolerate" it?

All good questions.

Science "carried out in private" is burdened by many of the same concerns (reproducibility, transparency of tools, lock-in, etc).

But isn't Science carried out in public, by definition? What about peer review? Has Mathematica become (like Windows aspires) the required "pass" to participate in scientific process?

Wolfram Research has never been a transparent company. I think the dangers pointed out by Jordi are real, and vastly underestimated.