This single page would have both great on-site and off-site SEO. Just as any other full site. The only difference is that it is a single page. The only con I can think of is that there is no internal linking between pages.
Also it is important to note this is not squeeze page or anything like that. The page would be full of helpful content that would truly be better than the pages of websites currently being ranked for that keyword in the SERPs.
Any advice would be helpful thanks.
For example: I have a website. It is a single page site. That website is http://www.kellygaskins.com/ (this site is a site for a missing friend.) Technically I am the authoritative website on this 'topic' I rank in the top 1 - 3 spots of Google for keywords such as:
irvin williams missing
jenna and kelly missing from north carolina
kelly gaskins genny
kelly gaskins mexico missing
kelly gray gaskins found
missing irving and kelly mexico
missing person Kelly Gaskins
This page is a single page website. BUT it has a navigation menu to certain key parts of the page. Does this matter?