@tonl, #41: for a german native speaker, "Schön" at the beginning of a town name is just a prefix, an addendum, an additional specification, to which the proper name is to follow. That's why "Schön" is not accentuated, as a rule: Schöneiche near Berlin, Schöngeising near Munich, or Schönheide in Saxony mentioned by you.
An exception might occur if the proper name after "Schön" is very short, e.g. Schönberg. But for an exception from the exception, see #38.
The same applies to "Groß", "Klein" (Kleinkleckersdorf, an invented name used frequently for an arbitrary unimportant small village), "Hoch", "Nieder", "Ober", "Unter" and even "Wald" (Waldmünchen)