In a recent game we had a situation where Luke did his thing and was quite close to the edge of the board. The imperials had most of their units left to go and a few trooper/sniper units focussed fire on him, only doing 1 wound damage but adding 4 suppression tokens. Then Darth activated with Master of Evil putting 3 more on Luke (Rule question: I assume Luke counts as a trooper and we didn't play this wrong?).

End of round Luke loses 1 token leaving 6 and if he fails to remove any more during his rally step he panics. That would result in a full speed single move towards the edge of the board and Luke leaving the battle field.

As it happened Luke managed to remove 1 more token during his rally step to not panic, then spent an action doing a recover to remove the lot. However, had the dice roll gone the other way, that would have killed Luke off.

Is it correct that a panic'd unit has no way to end their panic other than the loss of a token at the end of a round and the hope you roll well during the rally step?

That got me thinking. In many games I've seen Luke (or other commanders) activated early on to do their damage before any suppression is added and the risk of losing an action occurs. However, if you're near the edge of the board, perhaps there's an argument for delaying the activation of your commander. If your opponent does then try to out suppress you (especially during a Master of Evil turn), you can activate at a point where you've got 3-4 suppression tokens and either roll well in the rally, or with your single action at least perform a recover to ensure there's no way your opponent can panic you and get a wound free kill.

Even though I think we've managed to not play suppression correctly in just about every game, from forgetting the +1 cover it gives, to forgetting to deal it out, I find the mechanic fascinating in how it can impact decisions made in the game. It really gives that covering fire feel too.

All correct.

And Suppression is the most important thing to remember in this game. If you go for it, you can ruin your opponent's plans

You played everything correctly and Luke would have run off the board had he failed to remove any suppression.

But in fact there are a lot more options to prevent units with lots of suppression tokens to run away. One would be to use the inspire keyword. Then there are some tricks with command cards: Jyn's Complete the mission ignores panic, Leia's No Time For Sorrows might push you far enough away from the edget to not run off the board, Luke's Return of the Jedi card removes Suppression (yes, also his own), ...

To actually scare Luke off the board is quite hard, but panicking in general is a solid and impactful part of the game.

I've had some close games with panic due to the commander not being close enough. I don't think I've ever seen Luke Panic.