I don't understand the hate Thomas gets for getting visibly frustrated. The fanbase complains "Kyrou doesn't look like he cares" and now Thomas cares too much. There is plenty to complain about with how bad the team is without nit-picking the mannerisms of its best players.
I think there are two-flavors to this:
1.) Concerns over long-term leadership.
2.) Fowler made some comments prior to the Armstrong presser about teammates being frustrated which 'leak into the team'. Thomas has become the assumed poster child there. Blues Twitter/Facebook is all over this and ready to ship him off.
Point 1 is a legit conversation. Counterpoint would be that McDavid, MacKinnon, Draisaitl, Tkachuk, Toews, etc. are all pretty emotional leaders. It's not without precedent, but its worthy of a conversation
Relating to Point 2: The moment that stuck out to me, last night, was the body language when Parayko dumped it in in OT...Thomas lost the puck but got into position to get the pass from Parayko and was very clearly frustrated at him for dumping it in.
If he's frustrated with teammates behind the scenes, then I think we do have an issue that needs addressed. I tend to think that's not the case, and that this is him bearing the weight of this team's (and his individual) failure, amped by Armstrong's press conference.
Ultimately, I'm with you - assuming he's not a tyrant to his teammates, I'd rather him care too much than too little. I suspect coaching feels the same since it's clear they haven't asked him to suppress any behavior.