Automatic call audio routing still asking for device
Ok, so it is a bit awkward, but I managed to solve my own problem. I went to:

Bluetooth settings -&gt; MyAirPodsName -&gt; forget this device


Then I paired my airpods again with my phone and tried to make a phone call. And sure it worked! Now when I have my airpods connected it chooses them automatically, if not, I can switch between "iPhone" and "speaker" as they are named in the list by tapping the speaker button. 

I think it is some weird bug that prevents the call audio routing from selecting the device automatically so you have to select it explicitly everytime you call someone... It is a bit annoying, but it is easily fixable, so no big problem.