Thinking about this some more, I'm not sure if fixing it for this English possessives wouldn't cause problems for other things. There are things in English that should be capitalised after an apostrophe, with O'Clock being an example (if using title case), and names like O'Conner being another.
Using apostrophes as quotes around words is another case where you'd want a character after an apostrophe to be capitalised, but could be treated specially since it's always at the start of a word.
Treating 's and 't at the end of words specially might work in English, but may be very wrong in other languages. So I am not sure it makes sense to change, unless it's part of the locale or something you can override yourself in some way.
If you want special capitalisation rules, the option of using a rename script is always there. That is exactly what was done to get proper English title case rules, where special words like "of" and "and" are not capitalised. (Titlecase rename script.)