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Smart courts lynch people whose logs only seem to target dead people. Yes, this occasionally leads to a mislynch, but it gets increasingly implausible as the game goes on.
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An N1 peek is a dead giveaway (the one time I saw someone try to present a will for it, the response was a unanimous “lol, N1 peek” followed by a lynch.) At the very least you’d wait to N2, after the first conversion and kill, since that drastically increases your chance of hitting an evil. Even then, the reality is that most real Observers end up not peeking much, so a will that uses it aggressively is instantly super-suspicious - partially because a real Observer is going to want to witness lots of visits so they can prove themselves.
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Most importantly, even if they spot neither of those things, you’ve forgotten that the Observer sees visits to their targets, not just by their targets. All it takes is one person saying “wait, I visited X that night, why aren’t I on on there?” Unlike Butler / Drunk logs, an Observer log can be contradicted by anyone who visited anybody you claimed to target, which you have no way of anticipating or knowing about. No amount of paying attention or planning can let you avoid this - every lie in your Observer will is another roll of the dice on whether or not a living BD you’re unaware of visited that person that night.
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Smart courts are going to know what’s already been said. My response when someone presents an Observer will is “can anyone confirm this?”, and I check my own detailed logs to see if the confirmation is something that was already public information. If nobody confirms a new, previously-undisclosed visit, you hang. A real observer log will almost always have lots of confirms from people who haven’t spoken up before.
I have never seen anyone successfully fake Observer - not once, not in all my time playing the game. Even in the outlandish situation where you manage to get past all of the problems I listed above, I would still say you succeeded primarily by (extreme) luck and not skill - again, it only takes one stray visit to blow your whole logs apart and get you insta-lynched. (And, of course, any claim, no matter how far-fetched, can get past a sufficiently careless and inattentitive court - but we can’t balance the game around that.)
Like, can you theoretically claim Observer? Sure, in the same way that you can claim Noble and hope nobody asks you to use your abilities. (That’s why I called the category “basically impossible” rather than “literally impossible.”) But it’s not really a realistic option against competent opponents.