Your thinking is sound, however, your technical understanding of subdomains seems a little off. For example, in the URL www.allinfo.com, the subdomain is the “www.” part of it. In your example, “www.allinfo.greenwidgits.com” the primary domain is “greenwidgits.com” the “all info” is a subdomain of greenwidgits.com, so you would need to purchase that domain separately from the allinfo.com domain.
Search engines do not “rank” sites, they rank individual URLs. So it would be just as easy to rank a page on a subdomain as it is for any other page. Your idea is a sound strategy that will save you substantial dollars. How well you do will depend on the quality of your content and how well you promote it. The fact that it is a subdomain will have little or no impact at all. For that matter, you can do nearly as well using directories, all on the same domain (i.e. www.allinfo.com/greenwidgits/, www.allinfo.com/getridofsquirrels/, etc.)
Don’t get caught up in the misconception that search engines rank sites, that will cause you to do a lot of stupid things that waste time and money.
Instead you could create a “green widgets” subdomain of your primary allinfo.com domain (i.e. greenwidgets.allinfo.com”, getridofsquirrels.allinfo.com, etc).