Personally I love Mccoy, despite him being a bit.. racist against Spock. (Spock is my heart character). Mccoy is a grumpy, sarcastic and funny guy. He can be mean but he's nice deep down. Also he wants to save people. The trio would not be the same wihot Bones. He's awesome.
I think the reason the bickering isn't "obviously a joke" is because it isn't always a joke for either Spock or Bones. Bones is a very emotional character. He strikes me as something of a sci-fi hippy in some ways. He truly disaproves of Spock at times, but he loves him all the same. I love this about them, because that's often how family members are.