If the writing wanted Carl to come off as reasonably cautious, the way you are saying, he would have been patiently sitting in the woods for the fight to end. I would have had no problem with him killing the dude if Carl hadn't said 'I should be there' and then the scenario played out exactly the same otherwise.
But the inclusion of that single line turns Carl from a cool headed survivor into little Shane.
And Shane was a serious asshole that needed to die.
I understand Carl's motivation, too. He's seen Rick be merciful/honorable/kind and it's bit the group in the ass many times. Also, Carl sees himself as making all the decisions to protect the group and 'doing what's necessary.' And Carl acted entitled in this episode. As though he had the right to take life because of what he does to protect the group.
All of this is exactly what Shane was doing. And it's all the more frustrating because all of this stuff is happening to Carl while Rick is going through a rough stretch and dealing with a lot of stress, and his head isn't in 'the dad game.'
It's actually really good writing that has three seasons backing it up.
I like the development because for me, the show is and always will be about Rick and Carl. The rest of the characters are just there to enhance that relationship. It could be Michonne, Daryl and Herschel or it could be Boba Fett, Robin Hood and General Zodd. They will still always be second fiddle to Rick and Carl.