I don't link to the home page from any of my footers, so I have no idea if it's a good or bad thing as far as ranking go, but I haven't had any complaints because it's not there.
If we do link to our root index in the footer should we rel=nofollow our own in-site link?
Absolutely not... As soon as you nofollow a link to a resource on a page all links to that resource on the page are nofollowed, so a nofollow on the footer link would also effectively nofollow the header link and the breadcrumb link and every other home page link on the page. *
It actually makes sense to do it that way from a search engine perspective when you think about the intent of nofollow being to say, 'This link was not included editorially reasons.' or 'I'm not 'vouching for' the resource linked.'
If you indicate the resource is not included for one of the preceding reasons via nofollow on one link, then how can the rest of the links to the same resource be objective, editorially placed and to a resource you trust?
It makes no sense to trust/vouch for/editorially link a resource with one link but not another... Either the resource is something you vouch for and/or included for editorially reasons, or it's not.
* I don't have time to go digging through history to cite a source for this, so you'll have to DYODD to verify what I'm saying has been posted here and I believe included in at least one MC video on YouTube.