Hello Ted, yes they can hurt your site in a number of ways. Site owners tend to make these links anchor text rich, so if you've got a link in your footer saying 'Blue Widgets' then effectively you may have 30+ anchor text links from your own site. And yes, anchor text backlink ratios are calculated with the inclusion of internal links from your own site.
As you also mentioned, these footer links are draining the juice out of your main contextual links within in your main page's copy. Effectively, those nice internal silo links you send to your inner pages are being watered down by all of your dofollow footer links.
So do I make all of my footer and menu links no-follow then? And there's the problem. You won't find definitive answers on this because it's grey hat. Google will tell you that nofollow links are links that you don't want to vouch for. So are you going to send a signal to Google that tells them you don't trust internal links on your own site because you added the nofollow attribute to them?
And yes, whether the link is nofollow or not, it's still included in your overall anchor text ratios.
Now we move into PR sculpting. Google will tell you not to do that, and that PR sculpting doesn't work anyway. Is that because it still works very well indeed? Why are there so many authoritative sites that still use the nofollow attribute on some of their internal links? Don't they trust these internal links, or are they channeling link juice to the pages they want it diverted to.
If the rest of your link profile was pretty clean, and all of your offsite SEO was above board, then I think you'd be pretty unlucky to get a penalty from internal links coming from the footer of your own site.
One of my sites is ranking top three for many medium to semi-hard keywords that uses PR sculpting. Every single menu and footer link is nofollow. So the homepage has about 30 nofollow internal links on it, and only two contextual links in the main copy that link to the other inner pages that I wanted to rank.
That site has remained top 3 for over 1.5 years now without a hitch. This definitely isn't conclusive evidence by any means. The site itself is very strong and has great content too, but it seems as though all of the nofollow links haven't affected it negatively. And the inner pages that I sent all of the juice to are ranking #1 too. In my opinion PR sculpting does work but I also think it's dicey.
In your situation, I would maybe just dial down the exact match anchor text and change them to partial match links. Google do devalue your internal footer links to a certain degree but there's no black and white answer. If your site is big, then your generating 100's of anchor text links, and although they're devalued, it's still a bit dicey.