Changing default email reader does not take effect
I had this problem too, when trying to set Airmail.app as my default email client.  I found a solution (after many failed attempts) here:

http://docs.airmailapp.com/airmail-for-mac/setting-airmail-as-the-default-email-client-airmail-for-macos

All credit goes to the author of that article, and the instructions should apply for any email client, not just Airmail.

The key is to reset Apple's LaunchServices database before opening Mail.app.  Here are the instructions from the above-linked site (slightly modified):


Open Terminal (Cmd+Space Bar and enter Terminal)
Copy &amp; paste this command:

/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -kill -r -all local,system,user

Press Return to submit the above command and wait for it to finish (might take a few moments)
Open Mail.app and set your default email reader


This worked for me.  I noticed though that, when right-clicking a file in Finder and choosing "Open With", the menu was very slow to be populated with a list of apps (note that the LaunchServices database also controls this list).  So I restarted my computer and everything was fine.