And in general, there surely is a way of formally saying "this is theoretically X, but effectively Y, for the [hand-waves] kind of inputs"?
That said, some simple intuition is the following: PSPACE is a subset of EXP is a subset of EXPSPACE
(We think these are all strict separations but technically that’s not fully proven)
If you use the shorthand intuition that we can handle polynomial scaling but can’t handle exponential scaling, this means that we hit a time barrier (EXP-complete problems) before we hit a space barrier (EXPSPACE-complete problems)
Another bit of intuition: you can store a very big number in very few bits in binary because binary holds an exponentially large number in linear bits. But you can’t loop over that number in a humans’ lifespan.
Edit:
> they can be treated as Turing-complete for a subset of programs that are well-behaving - i.e. don't end up hitting the memory limit
Just to be clear, it’s a matter of input size and not the programs themselves. Technically you could say we haven’t “solved” sorting on real hardware because nobody can sort the first 2^1000 digits of pi. But realistically we don’t care to do so.
For the arguably part: I am assuming that the machine can access all of the input at once, so it is reasonable to expect available memory to be a multiple of the input, so you get O(n) memory.
Usually people just let it go unless someone brings up specifically something that implies that there is, or might, not a shared mutual understanding (as done here). Maybe it is shared, maybe not, maybe someone reading it doesn't understand the difference. I mean we're humans. We compress a lot of information into language that is not directly expressed in our words (this is also why it is often hard to talk to people on the internet since there's a wide audience with vastly different priors. Relevant XKCD[1]).