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Lucy is not only a nickname, but a name in its own right, as in, St Lucy. I suppose Ella exists in its own right as well, by now.
Apart from that, all the names you mention are only nicknames for me, of Anne, Elizabeth etc. Most nns, especially the ones ending in -ie, don't really look great on adults, especially in professional/formal contexts, they're just too childish.
I think it's better to have a "real name" on the dotted line, parents can still use the nickname but leave their child the option, what's the big deal?
Some nicknames, such as Ed, Tom, Kate, look ok on adults, but I still think it's better to have a full name anyway.