You only get the scans if the seer tells you. You do lose something, an extra life for the most important goodie in the game. And that extra life can be a big deal - here it allowed Johho and Nautilu to be turned into an ersatz JL, rather than werewolf chew toys. It improves the odds of your side winning, which is just as necessary to you winning as your rival being dead. The question is which condition is harder to achieve - I think team win, you think rival dead.
This is all assuming the seer scans you though, which didn't happen the two times I've seen seer-apprentice rivalry. An interesting approach would be to look to be scanned by the sorceror, based purely off a guess you're an apprentice rival to the seer. That might get my endorsement as clever play.
You don't lose an extra life, the village does. From your perspective, when you lose your life, you're dead. You don't have any extra lives, your (or your master's role has. Team winning, conditional to you winning, is not necessarily or even likely to be made harder because you got rid of the Seer.
That approach isn't likely to work, because the Seer would likely put you up as a priority for being scanned.
If you don't get scanned, it is usually because the Seer is already trying to find a way to get rid of you, and thus is not interested in wasting the scan.
I would probably still scan you, just in case you happen to be a cultist (and I'd be a Priest), so I could expand my options to get you killed without compromising my position.
Again, let me try to put it in a clearer enunciation. You are an apprentice, and you want to win, and to win, you need to kill the Seer, who had you scanned and claimed.
So, scenario 1, Seer dies and you take over. The village still has one Seer, so no change in scanned guys, and no backups for that Seer, which, in your perspective, is totally irrelevant, because
when those backups apply, you have already lost, so we can exclude that from our reasoning.
Scenario 2, Seer doesn't die and he doesn't kill you. The village still only has 1 Seer, with a backup. From the
perspective of the village, it is preferable to scenario 1 and 3, but from your perspective, it is not, because you are
further away from victory, and the Seer likely has more clout than you if he wants to get you lynched.
Scenario 3, Seer doesn't die and he kills you. Game over.
Scenario 4, Both you and the Seer die.
So, from your selfish perspective, scenario 1 is clearly the best, so it makes sense to strive for it. However, there's a small danger to fail and trigger scenario 4, if both the Seer and the rival get each other killed. Nevertheless, your optimal choice, regardless of what your rival does, is to try to get your rival to die. If your rival doesn't do anything, you win (by now being with nearly the same (-1 villager) base chance of winning, probably even with better chances due to the impact of a Seer death in the game). If your rival does the same, you lose, but you would also lose if you didn't do anything, in that situation. Which is why I referred to the Nash Equilibrium and game theory.
