I think there's also the fact that Ichi was on the D1 mislynch and off the D2 correct lynch (like Eevee). That's another point against him.
As for safe claim/smart claim/etc. -- Ichi claimed under pressure. I think he took a chance and claimed a PR hoping to survive.
I am arguing that, AT THE TIME OF HIS CLAIM, he made the safest claim he could if he is a Traitor in TKM. If he is a Traitor in TKM, he knows there are exactly three roles NOT in the game. He chose the one with the easiest to fake results. For all I know, he shot me and I was saved by Silver's jailkeeping, and he claimed to investigate me to cover bases (although there's no tracker...it's always best to use as much truth in your lie as possible).
I feel like you are arguing that he had a 50% chance of claiming a role that could not exist when the three real PRs became known. But at the time that he claimed Psychologist, any single other PR in the game at the time would know that a psychologist was possible.
Remember, no one else had claimed. If he's the Traitor in TKM, the only way his Psychologist claim is immediately caught is if a BP Townie exists. A JK, Detective, Commuter, or Bodyguard all have options for setups with a Psychologist, so they can't immediately out him.
So it was a 1 in 5 chance he gets caught immediately. 20%. Not great, but better than dying. If he claims Goon Cop, it doesn't work with Jailkeeper OR BP townie and he knew the JK existed, so that's out. If he claims Watcher, it doesn't work with Detective or Bodyguard.
So Psychologist was a 1/5 chance of failing immediately. The other two available fake claims were a 2/5 chance of failing immediately. Ergo, if a Traitor in TKM is going to fakeclaim a PR, it has to be Psychologist. (Good to know if this setup is run again, btw)