Of course they would worry about martyrs. Remember what happened during the war meeting--Zuko discussed that the Earth Kingdom people won't give up as long as they have hope, showing that the spirit of rebellion remained strong and stubborn, even with the Avatar seemingly dead.
You remember Ozai's response to that? It was "burn 'em all." Ozai's politics aren't about taking the soft approach to avoid resistance, if resistance springs up, Ozai's reaction is to just keep hitting it harder until it's destroyed. The politics that defines the Fire Nation's military is using rapid, overwhelming force to destroy the opposition.
In a way, the Avatar DID become a martyr, and that didn't fare well with the Fire Nation forces in the Earth Kingdom.
I'm not so sure about that, but either way, this is the fallacy of consequences. Even if Aang's apparent "death" DID galvinize people & contribute to the downfall of the Fire Nation, it doesn't follow that the Fire Nation was afraid this would happen. In fact, obviously they weren't, or Azula wouldn't have tried to strike down Aang & Zuko wouldn't have been praised by Ozai for supposedly being the one who did it.
Who says their secondary goal shouldn't have been to spread resistance, as in second to helping Aang master the elements?
Because mixing competing strategies doesn't actually make them stronger, it actually weakens both. Say they're in an area for a few days. It can't be longer than that, because Sozin's Comet arrives at the end of the year, & they need to make sure they have enough time for traveling & training.
Maybe they might get lucky here & there, but most of the time, that's just not going to be enough time to raise a strong resistance. But it's plenty of time for their supplies to run low. They've barely accomplished anything in the B Plan & have caused a huge setback to their A Plan. But in a way, it's actually luckier that they failed, because at least the Fire Nation won't call in more reinforcements that will make it harder for them to get around.
To put it another way, it's like if you're playing baseball & you decide it's a good plan to have a bat in both hands, because that'll give you twice as many chances to hit a home run! Well, no, it's not a good idea, there's a reason pro baseball players don't do this. In reality you just lose most of your accuracy & swing each bat with less than half force. It is actually better just to put all of your resources into just 1 bat, it maximizes your chance of success.
They would've been the voice of resistance, while everyone else would do the rest and follow in their example. It's not much, all they just need to do is let people know that fighting the Fire Nation is possible.
No, it's not that simple. You can't just tag a few posters & cause a rebellion to spring up. It requires meeting with community leaders, exchanging plans, giving them any training they might need but not have, knowing how this will all be organized without being caught, finding out who can be trusted. It takes time & it takes effort.
Yes, Team Avatar knows how important it is to help Aang master the elements, but they never lose sight of the bigger picture. Even Katara makes it clear that no matter what, they cannot turn their backs on people, and they still need to fight the Fire Nation for those who couldn't.
Which, as I said, was not an argument from pragmatism. You could make the argument that they "should" do it regardless of the consequences, but from a strategic standpoint, it's not a good plan.
Someone has to do something about the injustice and terror the Fire Nation was spreading. This rhetorical question always comes up--"if we don't stand up, who will?" Without hope, we have nothing.
There's also the saying, "Those who fight & run away live to fight another day." It might not feel good to have to strategically retreat from a situation, but in the long run, losing the battle might mean winning the war. As opposed to the possibility of trying to help everyone & winding up helping no one.