Unicode normalization was created to facilitate string comparison
of different representations considered equivalent. As been noted
on this list many, many times before, the equivalence defined by
normalization is useful for some purposes but not others, and that
this notion of "equivalence" is not something universal: there are
pairs of sequences that some would perceive as equivalent that are
not, in Unicode formalism, canonically equivalent, and other pairs
that some would not perceive as equivalent but that are, in Unicode

Canonical reordering and normalization forms are perfectly suited
to, say, defining valid IRIs or other identifiers. But that's not
because these formalisms provide some universal notion of equivalence;
rather, it's because the specifications for such identifiers have
been defined in terms of Unicode normalization. And, yes, that's
all very circular.

I mentioned issues for scripts beyond Latin, Greek and Cyrillic. A
few people have replied to me off-list pointing out how normalization
even presents issues for Latin. I will extend what I said earlier:
even for Latin, normalization can create significant usability
challenges in relation to text input and editing.

Ǟ  01DE LATIN CAPITAL LETTER A WITH DIAERESIS AND MACRON
ǟ  01DF LATIN SMALL LETTER A WITH DIAERESIS AND MACRON
Ǡ  01E0 LATIN CAPITAL LETTER A WITH DOT ABOVE AND MACRON
ǡ  01E1 LATIN SMALL LETTER A WITH DOT ABOVE AND MACRON
Ǻ  01FA LATIN CAPITAL LETTER A WITH RING ABOVE AND ACUTE
ǻ  01FB LATIN SMALL LETTER A WITH RING ABOVE AND ACUTE
Ấ  1EA4 LATIN CAPITAL LETTER A WITH CIRCUMFLEX AND ACUTE
ấ  1EA5 LATIN SMALL LETTER A WITH CIRCUMFLEX AND ACUTE
Ầ  1EA6 LATIN CAPITAL LETTER A WITH CIRCUMFLEX AND GRAVE