There are times when indices need to be tightly packed (mesh geometry for example), where its useful to store indices as u32 instead of usize.
u32
usize
No.
If it were your own type, you could implement Index, but it isn't and you can't.
Index
If you're really, pathologically opposed to casting the index, you could write an adaptor type that does the cast, but that's getting a bit silly.