Both problems are missing the point: you cannot handle Unicode correctly without locale information (which needs to be carried alongside as metadata outside of the string itself).

To a Swede or a Finn, o and ö are different letters, as distinct as a and b (ö sorts at the very end at the alphabet). A search function that mixes them up would be very frustrating. On the other hand, to an American, a search function that doesn't find "coöperation" when you search for "cooperation" is also very frustrating. Back in Sweden, v and w are basically the same letter, especially when it comes to people's last names, and should probably be treated the same. Further south, if you try to lowercase an I and the text is in Turkish (or in certain other Turkic languages), you want a dotless i (ı), not a regular lowercase i. This is extremely spooky if you try to do case insensitive equality comparisons and aren't paying attention, because if you do it wrong and end up with a regular lowercase i, you've lost information and uppercasing again will not restore the original string.

There are tons and tons of problems like this in European languages. The root cause is exactly the same as the Han unification gripes: Unicode without locale information is not enough to handle natural languages in the way users expect.