A small business owner with a static site wants to move hosting and doesn't have their website files and/or login to their old hosting account.

Typically in this case unless you can get the old files off archive.org (which surprisingly you can although pages are often missing) the customer is stuck.

1) I propose a service whereby the sites of major hosting providers are slurped and archived in there entirety (remember these are static) to aid in at least having a starting point to site recovery and moving.

2) Case #2 would be the customer has the files and/or access to the old hosting account and just needs handholding which the new host doesn't provide.

My feeling is that this (in addition to moving sites which are still active) would be something that hosts would welcome if they don't offer it themselves.

Mediatemple offers a similar service:

http://mediatemple.net/sitemover/