There is a fix for that! What you need to do is sign into your YouTube account's advanced settings and set the default to the channel that you want to insert videos from. Read on for more detailed instructions.
One of the advantages of using a whole array of Google products is that they are usually relatively easy to integrate with each other. For example, if you use Blogger as your blogging platform, you can insert an image from your Google+ Photos or insert a video from your YouTube channel, as long as you sign into Google+ or YouTube with the same Google account as you use to sign into Blogger.
• make sure you are signed into Blogger with the same email and Google account that you use to sign into your YouTube account
• make sure that you have your browser set to accept 3rd party cookies
Then you need to set the default YouTube channel for "Signing into older apps":
Note June 2014: it is now easier to set a default channel for your YouTube account - please see the new updated instructions
• Sign into your YouTube account.
• Make sure you are using YouTube as your Google+ Profile identity. If you need to switch, you can do so at www.youtube.com/channel_switcher
• In the drop-down menu under "Signing in to Older Apps" select the YouTube channel you would like to post videos from.
• Be sure to click the blue "Save" button in the upper right hand corner.
Now you can go back to your Blogger post and click Insert Video.
When you select "My YouTube Channels" you should see the videos from the channel you selected in your YouTube channel's advanced settings.
Note that Blogger does not currently indicate from which channel "My YouTube videos" is displaying.
If the videos you see there are not the right ones, you may need to go back to your YouTube channel's settings and make sure you've selected the correct channel.
And if you want to insert videos from different YouTube channels in different posts, you may want to get the video embed code from YouTube, and paste it directly into your blog post.
Blogger Help: Posting a video from YouTube
YouTube Help: Use third-party devices, apps, or tools with channels linked to Google+ pages