The "meditating on death" sounds like it's meant to be a meditation on impermanence, and on the unattractiveness of the body (i.e. an antidote to lust); as well as on the "just seeing" and so on that may be an antithesis to a excessive mental fabrication.
But there may be another aspect to it (beware this is something I've been thinking about myself, and is not a thought that I've been reading or hearing about from others, so don't take this as an authoritative answer) which is 'real' in a different way: which is to do with how you handle time.
If you consider not time but money for example, if you borrow money then that's a burden. "How will I pay the money back? I owe the money, I spent the money, how can I accumulate more money (more than I need) to pay back what I owe?" If someone says to me, "Would you like to...?", or, "Can you...?", if I have a debt then maybe I'm meant to say, "Sorry, I owe a lot of money and instead of doing that good thing you suggested I have to work to try to pay it back." In any case that doesn't seem like sukkha.
According to this one of the questions they ask someone who wants to be ordained is, "Are you free from debt?"
I think something similar happens with time: if I accumulate a time debt, if I have a lot of things to do, which I haven't done and which I need to do, which I owe to someone, then maybe that's not conducive to being free (in the "liberation" sense of enlightenment), it means that you're unable to do what you want or should.
So I think that it may (at least for house-holders) be (not a mind-construction or reality-distortion but) a sīla practice, which ties into the notion that a result of virtue is the lack of remorse. I think a consequence of "living each day as if it's your last" might be that you have done (and continue to do) everything that you need to.
It might fit into the notion of karma too, somehow: if you go around saying, "Sure I'll (promise to) do this, that, and the other..."
I'm not sure if you are even answering the question, but it doesn't matter.
To try to even answer the question, then, the "last day" doctrine or something a bit like it might be traditional in Zen -- see Three Days More.
I was watching this video recently which I think is introductory Zen (if you don't have time for all of it, try up to 10 minutes from time 29:00 onward).
Or see also the subsection titled "Yes, I Speak Zen" in A Still Forest Pool which ends, "Perhaps the Zen student glimpsed that the heart of vipassana is no different from the heart of Zen."
IOW I'm guessing that the point of "live this as your last day" is meant to be the opposite of "pretending" -- for example, the intention isn't, "pretend that now is tomorrow and that you are dead" -- instead maybe the intention is, "tomorrow is not now."