The Unicode way makes sorting easier. Your way would require special knowledge about the characters to know that ä should sort directly after a, rather than directly before ë.
But I do suspect it had something to do with ascii compatibility, I don't recall what. Very little of unicode is accidental, there's usually some reason for whatever in it.
aa ah az ba bh bz ca cz ch
treating "ch" as a single letter that comes between c and d.
or
ab ah az b c .... z aa
treating aa the same as a separate letter at the end of the alphabet.
Then there's other rules for sorting that aren't directly alphabetic, like that names beginning with "Mc" should be treated as "Mac" or "St " as "Saint ".
"10 cats" should sort after "2 cats", not before it.
Anyone who tries to sort by just numeric ordering is doing it wrong.