If Avatar:Secret Of The Fire Nation has lots of romance then action cartoons are falling apart because Teen Titans:Trouble In Tokyo has lots of romance.
...Did you even watch either of them? Avatar had like, a few intimate moments between Sokka and Suki, but the rest were just little hints (Toph kissing Suki by accident thinking it was Sokka) or little flirts (Ty Lee acknowledging Sokka and Sokka waving back).
Trouble in Tokyo only had the Starfire/Robin subplot, but it didn't get in the way of the plot, nor did it make the action scenes less awesome.
Besides, I don't think there's any rule that prevents a little romance from action shows. In a way, it makes them more interesting.