Hezký as nice is acceptable for inanimate objects. House, car, shoes...
But when you say NICE about people in English you are talking about their inner beauty. About them being good pleasant people. Nothing to do with a shape of their nose or other features. HEZKÝ though only talks about what things look like. She can be pretty (hezká) but a completely nasty person.
Why handsome isn't accepted in this sentence? In some cases Hezka is pretty, but it accept handsome and for some reason in other cases it means handsome :/
In the time since the OP asked about this, we've been adding "handsome" as a valid translation for females as well as males, even though it's less commonly used for girls and women. It was missing for this sentence, and will now be accepted.
beautiful is stronger and it is the equivalont of a different word: krásný (/á, /é)