I had forgotten how prescriptive the 1e PhB is by RAW. It feels like it is going to invite the player to do some non-mechanical creation... "and possibly give some family background (and name a next of kin as heir to the possessions of the character if he or she should meet an untimely death) to personify the character." The DMG total power over secondary skills (if used) to the DM and that the age was explicitly random.
Does 1e even have ability check suggested like B/X does?
:-/ We were doing a boatload more adding of stuff than we thought!
And B/X and 2e were a lot different by RAW from 1e on the actually running the game parts than I remembered.
One thing that is helpful to remember is that this is very context-specific, which isn't apparent looking back.
OD&D (as in the original books) is unplayable unless you both have a firm background in the hobby as well as other supplements and knowledge. The very first issue of the Strategic Review includes advice about how basic combat is supposed to work in D&D. It was very much a hobbyist's game, with both assumed knowledge and assumed tinkering.
OD&D -> Holmes -> AD&D. 1e is effectively Gygax's standardization of OD&D. It is both "complete" and "incomplete" simultaneously, in that it provides the seemingly-schizophrenic advice to follow these rules, and make it your own. The reason for these contradictions is fairly simple; Gygax the hobbyist understood how the game would be and should be played, while Gygax the businessman was concerned about competitors muscling in on his territory. Anyway, you really couldn't run 1e by RAW, nor was there much of an assumption that you were going to. It was still a hobbyist product. It a player wanted to do something interesting, then they could!
Meanwhile, you have the separate and distinct B/X (Moldvay/Cook) which could not assume that prior knowledge. However, for legal reasons, B/X also had similarities going back to OD&D. So the new Basic line was compatible with the old Advanced line. But because knowledge could not be assumed, Moldvay and Cook had to include rules for the DM for adjudication, even simple ones like the one you excerpted.
But the vast numbers of new players didn't know all of this. So there was a mishmash of the various rules and rulesets.