I think it's still not the problem being solved here.

To my understanding, from conversations with people on the finance side of things, the point of this game is that:

1. If you get everyone to do their own expensing; and

2. If you set up a system that's robust against mistakes made by people with no understanding of corporate finance, which is almost everyone in a given company (that's the "if you don't get it right up front, the computer won't let you through" principle you mention); and

3. If you tell everyone to use it and that it's their responsibility to be good stewards of corporate money they have the privilege of using, etc.; then...

4. ...you get to hire less people on the finance side of things.

I think it's another case of large organizations chasing legibility[0], to the detriment of everyone within. It's similar to what a lot of other office/business software does: it lets the company get rid of a class of specialist, whose salaries are clearly visible on the company books, by distributing their work more-less evenly across everyone else in the company. This, obviously, causes everyone to lose productivity, as they're being distracted with work that's outside their specialization/expertise, but that only adds up to an "unexplained" overall small productivity drop of the organization (and the frustration of most employees) and is not clearly visible in the company financials.

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[0] - To borrow the term from Seeing Like a State.