It would be interesting if among the default character sets you also included one containing everything in
Unicode's BMP. Though it can't really be exactly everything, some chars are expected to be replaced by others or just plain ignored under certain conditions, and using the low and high surrogates correctly would imply that there is a severely limited number of possible characters imediatly after/before a surrogate, reducing the entropy of the password; so all those problematic codepoints would need to be left out to avoid producing weaker or just plain unusable passwords (i'm not sure what is the expected behavior in the presence of unalocated codepoints, perhaps those should be ignored as well; also, i'm not sure if it would be safe to include things like the BIDIR control characters or if they're expected to be replaced or ignored by some software.
And just in case there are some changes in the BMP in the future, the version of Unicode used for deciding which characters to use should be mentioned somewhere, and if possible, previous version of the character set should be included if there are changes.