As a former Teamspeak manager (for what its worth): I say -1 to this suggestion.
Communication in multiplayer games is essential, especially when playing with people who use the Teamspeak. By breaking the rules, not only you ruin the gaming experience but also provoke the need to "rage quit", ultimately leading to a person possibly not joining Teamspeak again or maybe this community. Its true that its internet and you have to be "mature enough" to be on it but like all the rules suggest, it is meant to keep players and make a welcoming environment for them.
In your case, a simple sorry could've gone a long way and prevented all of this from happening. And no I don't believe your ban was unjust, simply due to the behaviour you exhibited. The only reason why I am bringing your ban up is simply because you need to hear it from someone that isn't part of management.