Of course it is a personal benefit, you are literally benefitting by not spending your own post-tax dollars for something that goes into your stomach. However, there are legal rules that allow categorizing certain such expenses and amounts as a cost of doing business even though the manifest benefit is purely “personal”.

These rules have tightened up since the days of company cars and company houses “expensing” employee cars and houses as a tax advantaged form of compensation. If you try to do that now, that all shows up as “compensation” which is taxed. If you look at say Mark Zuckerberg’s yearly “salary” you will see that it is almost entirely non-monetary compensation for bodyguard services and “paying” for Mark Zuckerberg, the CEO, using the plane of Mark Zuckerberg, the person, and paying personal income taxes on that “compensation” even though Mark Zuckerberg was not paid any dollars (for that compensation).

The allocations you are provided and the manner in which you are allowed to spend them are generally considered “safe” from a accounting perspective. There is usually wiggle room above them if you are willing to more thoroughly document or finagle them, but that is extra accounting department cost to do things beyond the safe, well-trod legal path even if it is actually okay at the end of the day.

None of which is relevant for a $5 box of fibre bars, which fall below the de minimis threshold.

Please cite the de minimis threshold you are referencing. Here is a basic 67 page overview by the IRS on this topic [1] which does not indicate any uniform generally accepted de minimis threshold for arbitrary expenses, so you need to cite specific laws, regulations, case law, or generally accepted accounting advice to support your statement.

[1] https://www.irs.gov/pub/irs-pdf/p5137.pdf