I am not impressed with a site's host. I have redesigned the site and planned to launch it with a new host. Instead of doing that I wondered if I kept my original site, downgraded it to a free site and used it as a 1 page landing linking to sections in the new site (with new domain name) would this increase traffic? Or would it be better to transfer the domain to the new host? Is there something I'm not seeing?
For the record, your hosting provider will make no difference to your site's SEO unless a user is performing a country-specific search (such as using google.ca instead of google.com to search for Canadian based sites). So if you're not satisifed with your hosting provider, just switch hosts and move your Web site (domain name and all) to the new hosting provider. Furthermore, it's never a good idea to just scrap your Web site and replace it with something else, unless the site is new (and not yet established), since you'll lose all the benefits of the hard work that was put into the site in the first place. I also recommend against creating "landing" or "doorway" pages, or "single page Web sites" that just link to another site. Either way, if you do that (the things I recommended against doing) you'll not only shoot yourself in the foot, cut off your nose to spite your face, but you'll also face a likely ban from the major search engines anyway, depending on what you do (and how grievous the offense is).
Transfer the domain to the new host - if any pages have changed file-names, link from the old to the new. The age of the domain is a big factor in SEO: don't throw that out the window just because you aren't satisfied with the host.
1associate, Others have already spoken to the SEO benefits (or not) of this strategy. Instead of doing that, I will tell you that you should be keeping the domain registration separate from your host anyway. Move the domain to someplace like GoDaddy (if it is not there already), and keep your hosting account elsewhere. This way, your host cannot hold your domain "hostage" when they hear you would like to move your site to another Web hosting provider.