US News does change their formula most years. However, I expect these changes have little to do with trying to accommodate feedback in how to make a more accurate ranking of “best colleges” and more to do with selling magazines/subscriptions. If the rankings are the same every year, there is little motivation for the past customers to purchase the new rankings. If something is new and different, there is more motivation to purchase and see how things have changed.
Alumni giving is only weighted at 3% and has relatively little impact. My guess is removing alumni giving and class size has more to do with these being categories in which colleges are more likely to be caught lying. Following the recent Columbia debacle, USNWR has become more sensitive to these types of misrepresentation. Several other colleges have been caught misrepresenting these stats besides just Columbia, including some that are frequently discussed on here. For example, as discussed at https://www.berkeleyside.org/2019/07/28/uc-berkeley-kicked-off-the-u-s-news-world-report-rankings-of-best-u-s-colleges, Berkeley was removed from the 2019 US News ranking due to listing a higher alumni giving rate than actual.
In any case, the post you quoted defined what I meant by “arbitrary” in the following sentence. I don’t mean the weightings are selected randomly. I mean that they have no validity or verification that they accurately reflect “best college.” USNWR is a business, and I expect that they choose weightings that result in the success of that business via a larger number of sales/subscriptions. The names USNWR readers expect to see on top (output of formula looks right), with minor tweaks from year to year (reason to buy another) = more sales/subscriptions.