bitcoin sub-currencies? is this worthwhile?

[_jeremy]

I wonder if something like this is worthwhile. I'm also wondering whether it's technically possible, either on top of the existing network or as an extension. At the moment i'm more interested in the economic sense of it though, so i didn't post to the technical discussion forum.

Suppose Alice offers services online. Alice takes 1 bitcoin, and appends a pgp signed message to it which says "This coin was signed by Alice!".

Next, Alice distributes fractions of that 1 bitcoin in any way she likes - for example, as a frequent-purchaser reward to her existing customers.

Either coins outputted as fractions of an input with this message would retain the message, or it should always be possible to check whether a coin derives from that "root" alice+bitcoin.

In the future, Alice accepts these alice+bitcoins for her own services. She has effectively printed her own currency with the same transaction-security features of bitcoins. Exchanges could be established for trading between such sub-currencies or for raw-bitcoins.

Does any of this make sense? I know that sometimes companies or small regions print their own "local" currency. Are we in favor or opposed to being able to do something like this on top of bitcoins?