I found the same and this is SO frustrating. But, you can use a really hacky workaround:
Export the 7.0 site blog
Import this to Wordpress (you just need a basic free blog account)
Once it's imported, export the Wordpress site
Import the Wordpress export file into Squarespace 7.1
The page layouts won't be great and I haven't got the images across, but at least I have all the posts with their text and can save a lot of time and copy/paste errors!
If you have multiple blog pages in your site, you can even export multiple blogs from your 7.0 site into 1 wordpress site, and import them all back into Squarepace together. And then recategorise them into separate blogs again like this.
Note: If you want to maintain your authors on the blog posts make sure to have an exactly matching user in Wordpress for each author so it can map them