Is it acceptable to italicize a compound descriptor instead of hyphenating it?
There are two ways I have seen to solve the exaggerated compound descriptor issue.
If the description is in the form of something you might utter as an admonition, you can use quotes:
This is one of those "everyone shut up and go way" kind of days.
But if it is not in itself a statement someone might make, stick with hyphens.
This is one of those missing-the-bus-and-being-late-for-work kind of days.
These are not rules, and I don't think you'll find anything definitive on this, but it's what I observe from decades of assiduous reading.
I have never seen this usage that I recall. If it's done, it's surely not common, and so would at best be unclear to the reader.
I HAVE seen people put the compound in quotes, like:
This is one of those "everyone shut up and go away" kind of days.
I presume the goal of either technique -- italics or quotes -- is to eliminate the long hyphenated phrase. I can see that it is a little ugly, and in these word-processor-writing days, the computer may decide that the whole thing has to go on one line (depending on line-break settings), which can mess up margins.