Why would a merc ever publicly claim something other than merc in the current meta? It risks getting you killed if your claims contradict anything else, it requires a lot of time and energy to focus on faking your will, and publicly claiming merc actually serves to protect your target, both because people will be more reluctant to try and attack them and more reluctant to vote against them. (Even if a merc did randomly decide to do that - which I guess they can, comfortable in the fact that they can auto-prove any time they please - what does it add? The fact that they can auto-prove makes any sort of depth or deception related to the role mostly moot.)
Now, if mercs couldn’t auto-confirm, then they might have an incentive to lie, since merc itself would become a suspicious claim; and those lies would be interesting, since nobody could just instantly reveal the truth. But that’s a good thing! We don’t want things to be obvious or straightfowrard, we want there to be lies and deception and distrust so gameplay is deep and interesting.
But beyond that, again - I feel that you’re making the mistake of only looking at this from the perspective of playing a merc (and what makes things easiest / most fun for the merc.) The merc’s individual perspective isn’t too important; I feel that even without easy confirmability, it’d still be fun to play and possible to win as (they might need a few buffs, but it wouldn’t be a big issue.)
From the perspective of the meta, having mercs be a viable fakeclaim (late in the game, in particular, when there may not be time to follow up on a neutral) is vastly more important than making things easier for the merc. I don’t see how an easy-confirmable merc contributes to the game at all.
Again, a social deduction game like ToL is all about evils lying and people trying to unravel their lies. A class that nobody can fakeclaim and which has no incentives to lie doesn’t serve a purpose - and every role that can’t be fakeclaimed makes the game a bit less interesting, the strategies involved a bit less deep.
It also makes it easier to find the Mastermind or NK (since it is extremely unlikely any of them would be able to claim Merc under the current rules, you can instantly scratch someone off the list of possible Masterminds / NKs as soon as the merc outs themselves.) And that’s a much, much more serious problem than your concerns about keeping the Merc game easy, since catching the Mastermind and NK makes up a huge part of the gameplay. Mercs shouldn’t be able to easily remove themselves from the list of suspects.