Why does Mail.app take three minutes plus to open?
Let’s see what Mail is doing:

Run the following Terminal command to enable kernel symbolication: $ sudo nvram boot-args=&quot;keepsyms=1&quot;
Reboot your machine and don’t open any apps except for Terminal.
Open Mail and wait a few moments for it to reach its steady-state unresponsiveness.
Run the following command in Terminal, making sure you’re only running it during the window of time that Mail is unresponsive: $ sudo spindump -reveal -noProcessingWhileSampling
After waiting for 10 seconds to collect a sample and another minute or two to symbolicate and format, you’ll get a file in /tmp/spindump.txt that contains a stackshot of every process.
Upload the file to PasteBin or some equivalent place and we can take a look to see what Mail’s main thread is blocked on.