Though all indications are that Blogger's API still sucks because it does not allow image uploading, the blogging application I use, ecto, has worked around this by uploading my images to Flickr automatically when I drag them into my posts. This is not ideal, since it pollutes my Flickr feed with random images for my blog, but it's better than no images.
I'm going to stick with Blogger for this blog because I don't have the energy to move it and ecto in version 3 is now much more smooth about working around Blogger's image limitations. It also now supports tagging in Blogger.
If/when Tumblr supports apps like ecto, I will move the blog off Blogger.(UPDATE: Another way Blogger sucks with ecto and other third-party tools: If you have Blogger set to "convert linebreaks" in the standard online Blogger posting form, that setting will *also* apply to posts from ecto, even though they are sent in HTML via the API. When you change this setting to work properly with ecto, it makes all your prior posts screwy. Dumb dumb dumb. If your blog is short, just republish all your old posts via ecto and you are golden.)