I agree with your whole post, but there is a nuance here that's important. This fallacy becomes true in a project large enough to average out individual variance. If you need 5000 software engineers, you probably don't care about their individual traits (you might care about the selection process and aggregate traits, but that's another level up).
So at a certain level of executive, this fallacy serves them well. And it probably serves their reports (who might manage 750 people) decently. But their reports, managing 150 people, hear the language and see the behaviors of their bosses and emulate this belief in fungibility, and it really breaks down at this scale. Even worse for the next levels down, who might manage 30 and 5 people respectively. Yet everyone who sits in at an important meeting of skip-levels and execs sees this model used for resourcing.
A pattern I've repeatedly seen is companies will plan out the next few quarters of work and then assign some number of people, one person for one quarter to a project, two people for three quarters to another, etc. This process enables executives to make decisions about costs, priorities and project funding. This works for it's purpose, however, the roadmap creation and review process perpetuates the fiction that people are interchangeable, that people can be generically abstracted over.