I've seen several times on TeX.SE (example 1, example 2) that I shouldn't use footnotes in titles, with no explanation. However as far as I can tell the technical problems it would cause (the command need to be protected, a short title should be provided for the TOC) appear to be resolvable. So why shouldn't I do it?
There are two issues, (a) does it work and (b) is it a good idea.
(a) is the easiest part to handle, the main issue being that you don't want the footnote in the page head or table of contents so (as you mention in the question) you should supply a short from in the optional argument (even if it is just the same as the long form but without the note).
That will then work in the standard classes. If you are using some custom formatting which sets the title in some rotated coloured box surrounded in 100 levels deep boxing levels of tikz positioning then it's possible that the footnote will not be able to automatically migrate to the outer level, but if you knew how to get into that position you should know how to work around the issues, so using
\footnotemark where you want the mark and
\footnotetext somewhere where it works.
(b) is harder. Use of footnotes at all is very subject dependant. In the mathematical sciences a footnote usually denotes a last minute correction squeezed in at a late stage; so something to be avoided at all costs. So having a footnote in a chapter heading would just be weird. In other subjects footnotes are more common, I've seen biology and law documents where an average page seems to be half footnote text, which looks bizarre to me but is apparently the convention. So the answer to (b) will depend on who you ask.
I can only refer to the famous quotation in the TeXBook
Don't use footnotes in your books, Don.
JILL [KNUTH] (1962)
If you can't get agreement in the Knuth household about when to use footnotes it's probably too much to ask to get global agreement on the same subject.