It's not exactly that he doesn't think she'll do well as that he's not sure she'll do well, and his ninja-ness prescribes a pretty narrow reaction to dealing with death/killing/injury/etc. Like, he's probably the most comfortable with himself, Vincent and Jaina in those types of games. He doesn't necessarily agree with all of their reactions, but he trusts them to be able to deal with things in a relatively dispassionate way? But like, Obsidian for example—Neji respects him generally, and doesn't think he'd be bad at all to have in a fight, but actual trauma tends to break him, and turn him very protective and emotional. Kyouko can be ruthless, but she also gets sullen and withdrawn, and he doesn't really expect her to contribute a great deal usefully. Spitfire has struck Neji as too sensitive, in the past, and too willing to take on trauma he's not prepared for, which is a problem. He's not entirely sure how Inara would deal with that sort of thing, since she hasn't been in that situation yet like you've said.

Beyond that, he suspects that she might unbalance things with the rest of the team probably wanting to protect her. She's not really new anymore, but she's still the newest Iolite, she's well liked, she's not a combatant type. Particularly like Obsidian (who as noted above, doesn't always handle some people in danger well), Neji wouldn't expect to play as rationally with her in the game. But, I should add that includes him to a lesser extent, and is also a biasing factor in this. Neji would must prefer spare Inara trauma games if it's possible because he doesn't really want her to have to go through with them. And when it comes down to it, that's part of the reason Neji considers himself and Vincent pretty much the optimum team for trauma games anyway. He wouldn't ever express it that way, but he would rather keep most of the team out of that sort of mess anyway.

He... doesn't really mind if Vincent is exposed to nastiness or having to make hard decisions, etc.

ALL THAT SAID. OOC, I think it would be really interesting to see how Neji dealt with Inara in a trauma game, and how he'd react to her willingness to be ruthless.

Would Inara have not wanted to go the self-sacrifice route, if she were in the castle?