One of the features of blogs, which a lot of blog owners seem to take for granted, is the maintaining of the posts and structure of the blog. With a static website, you design the URL structure, and you publish the pages in the website to the URLs as you wish. If you link the various pages to each other, this requires that you keep a glossary, of the URL of each page.
The larger your website gets, the more painful a task this becomes. Make a mistake with one URL, and you have a broken link. Search engines don't like broken links - so if you want your website to be featured in search result pages, you want to minimize broken links.
One of the advantages of publishing a website, using a blogging platform, is the blogging infrastucture. You provide the title of a post, and the URL is created and cataloged for you. With a Blogger blog, you can use the "Edit Posts" menu as a catalog of posts, and their URLs.
The downside here is that Blogger controls the URLs of the posts. If you republish posts - maybe after you export then import them, or delete then readd them, or even change the Archiving option for the blog, you will end up with changed URLs. This was a challenge seen by a few blog owners this year, as they migrated their Blogger blogs from external hosting (FTP publishing) to Google hosting (custom domain publishing).
If your blog is indexed by the search engines, and you republish the blog, you're going to end up with broken links in the search engines, caused by changed URLs. Your prospective readers will click on an interesting SERP entry, and get a "Not Found". This won't encourage them to keep reading your blog, the search engines will drop the reputation, and you'll get less new readers.
This will also be a problem if you move hosting of your blog to another service. Even if you can transfer a (non BlogSpot published) custom domain to another blogging platform, there will be differences in how the URLs are cataloged and generated, for each blogging service. No matter what you do, you will end up with broken links, and decreased search engine reputation.
If you move blog hosting, this won't cause major damage to the search engine reputation - at least as badly as renaming the URL of the blog. The search engines will continue to index the blog under the existing URL. The success of moving blog hosting requires a minimised amount of broken links. If you contemplate relocating or republishing the blog, look at the URL structure of the blog right now, at the possible changes, and at the possible effects from the changes. Make your decisions objectively.