he needs advisers, and Troi was perfectly fine, especially when dealing with new races. It's not a military ship
Never said it was a military ship (now you're putting words in my mouth). Sure Picard needs advisors, but does he need a counselor during a time warp or a battle? The writers nearly eliminated Troi early on in TNG, and it eventually got to the point where the crew would get into tailor-made situations specifically where she herself would be specifically needed (frankly, not necessarily a counselor, either). Is it sufficient to warrant the ship's therapist as a bridge officer? After all, Dr. Crusher isn't one -- she has her own office, her own department, commands a higher rank, and is often herself crucial to first contact missions. In Crusher's case, she only goes up to the bridge if she wants to or if the situation calls for it. Does the therapist need to be on the bridge 40+ hours a week? Just how often do they run into new species and aliens? On a ship of 1000 people, shouldn't she have some, I don't know, appointments? Research? Etc. etc. During a crisis, you can bet someone's fiddling their thumbs, and it ain't Wesley.
Let's say you're a random Starfleet captain. Are you stuck in an anomaly and need a psychic? You get Troi. Are you stuck in an anomaly and you have a non-telepathic counselor who's every bit as good, if not better, has more experience, and is more decorated than Troi? You're SOL there, buddy, thanks to the writers creating just about the only time you'd need a "counselor" in such a situation.
By contrast (and I can't believe I'm doing this), let's look at Neelix. While not a pure counselor/scientist per se, he was pretty darn close to it in function, keeping up ship's morale, helping Janeway during first contact missions, being the go-to guy if you needed to talk to someone. All in all, like Troi. Yet how many times did we see him on the bridge during an anomaly or a battle? Very infrequently, usually because the situation never called for a morale officer.