The native Android phone apps are not well integrated as you discovered. An incoming call could be added to contacts then off to calendar to do such. But the native apps are weak to say the least. This area seems to catch new android users off guard. I'm running into folk that expected the android apps that come with the phones to be polished and full featured.

Nothing is farther from what we see today.

https://www.google.com/#q=android+crm is beginning search to find more but only you may know which works for you.