Actually, it does not, just like it does not come into play for Chess, or for Go, or for Othello.
"Fixed-limit Hold'em is easier to play because the decision tree is trivial"
Trivial? Write a bot for limit Hold'em and you'll see that the decision tree is not trivial. This is not Tic-tac-toe; limit hold'em is a fairly challenging game for computers, and it was only recently that computer players could even compete against the best human players.
"No-Limit Hold'em is another thing entirely: the decision tree is so huge that it's impossible to bruteforce"
Yeah, and the Chess game tree is impractical to brute force, and no Chess playing program actually attempts to do such a thing. Likewise with Go, and likewise with limit Hold'em. So what?
In general, the challenge with Hold'em (limit or no-limit) is not just the size of the game tree, but the branching factor. There are only four betting rounds in Texas Hold'em, and so the game tree is fairly shallow compared to Othello, Chess, or Go. On the other hand, just dealing the community cards adds a large number of branches, and in no-limit games the possible bets a player can make adds even more branching. This limits the utility of approaches based on exploring random paths.
This is not a problem of psychology, it is a problem of algorithms and of game theory.