I notice that the quick edit box for an existing post has a quote button, but not code, tex, or icode buttons. Meaning that one has to type the tags manually or go to the advanced edit page. Is this an oversight, or are there legitimate reasons for it?

This is the default behaviour for the quick reply box. Unfortunately, the code used to generate this box is super messy, and I've tried in the past to include these buttons. There was a problem I ran into, but I don't remember what it was (it was over a year ago). There's a previous thread in here about it actually.