Well, I can't answer why it's not available, but I can confirm that it's not a CLI issue. The CLI spec doesn't mention it (as far as I can see) and if you use IL directly you can create a generic attribute. The part of the C# 3 spec that bans it - section 10.1.4 "Class base specification" doesn't give any justification.
The annotated ECMA C# 2 spec doesn't give any helpful information either, although it does provide an example of what's not allowed.
My copy of the annotated C# 3 spec should arrive tomorrow... I'll see if that gives any more information. Anyway, it's definitely a language decision rather than a runtime one.
EDIT: Answer from Eric Lippert (paraphrased): no particular reason, except to avoid complexity in both the language and compiler for a use case which doesn't add much value.