This is really about "at home first" work rather than remote work. The prevailing model seems to be "don't come to the office unless we want you there" as opposed to "work from anywhere". I understand the reasons for why companies want you at home but local rather than remote, just saying it's very different that real remote working.
Why do the reasons for it matter? There's an office for the company and you don't actually do work there. You work remotely for the company vs in-office. The whys do not matter in the definition of you working remotely from the office do they?
"Work at your home office" culture still expects you to be in a predictable location and working predictable hours. Very similar to showing up to an office everyday.
"Remote" is closer to, "your location doesn't matter as long as you can perform your job".