There are a number of good reasons why it is impossible to provide the layout you are looking for with
multicols. Two important ones are:
As the name implies the code is supposed to support different column numbers on the same page. Now how wide should a footnote be? Full text width is ugly, but so is any other width, if it doesn't fit with the rest of column setup. Even if the spec would be reduced be just "one and two columns with balancing" it would still be ugly if you have, say, a single footnote (in twocolumn width) but the bottom of your page ends up being one-column.
multicols works by collecting a page worth of material and then splitting off the columns (and in case of balancing at the end potentially retrying many (hundred) scenarios to find the best balancing solution). Now this works by using
\vsplit is keeping footnote material inside the boxes. So by using this approach you can't use the footnote material as poart of the column itself (or taking part of the balancing). Now it is possible, of course, to use a different approach involving a collection of output routines that do all this kind of work on the main vertical list rather than safely with already gathered material in boxes. However, it would be a good factor more complicated and as a result really complex output routines typically limit themselves to solving restricted problems.
Now TeX is Turing complete as you mentioned in a comment, but this isn't going to help you much initially. It doesn't mean that it is feasible to program each and everything in TeX and even if it is possible you might end up dropping all or most of the functionality that TeX offers in one area and reprogram it in a fairly inefficient way yourself just to get over built-in limitations. Until quite recently the biggest hurdle was that doing that would also mean the processing would end up being incredibly slow or hit memory limits.
That situation has improved a lot in the last years and this is one of the reasons why it is now possible to come up with a programming framework (like
expl3) that provides that basis for expanding TeX's abilities within TeX. When
multicols was originally written it would have been impossible to envision that one implements a full blown regular expression parser in TeX (not technically but realistically) now we have one in
Bottom line, the design of TeX was made for single column documents, and anything that goes a lot beyond that was pretty much either impossible or only possible in restricted scenarios.
Nowadays, one could do better and we do have a different page design concept in the drawer that does offer what you are looking for. The catch is, it is not ready. Its proto-type is already from 2000, but back then it was still utopia, because of the speed restrictions it imposed.
That has changed, so now something like
expl3 is a platform that can be (and is) used for real, and we are currently in the process of revising the code and ideas from the end of the last century. Now this sound awfully old, doesn't it? But fact is, for current LaTeX
multicol is still around as "the" solution so ... there is some reason for that.