In what scenario, exactly, do you want to know that the text "ØÆÅ" is three characters long? That's almost never a useful question to ask or a useful answer to have.
According to the article, UTF-8 sorts lexicographically the same as UTF-32, implying that there is no need to know the length or character boundaries for ordering/sorting.
The others would be good reasons though.
All of those need pretty deep knowledge of Unicode in general and the language you're working with in particular. Counting "characters" (really, code points) is going to be the least of your worries.