That's because of 80s writing, not because of a fundamental flaw in the character. The Sopranos shows us that a psychiatrist character is a very useful storytelling tool if properly applied.
That's because that was a major element of the series. The show was about a mob boss who was having emotional problems and went to see his psychiatrist to deal with them. The same would only work for Star Trek if the show was about a Starfleet Captain who had emotional problems. And if the Captain really does have so many deep seated problems that he needs to see a therapist every week... then how is he captain in the first place? Tony Soprano only got away with it because he was a criminal and worked in a business which didn't require regular psych evaluations, and even then, if word had gotten out that he was seeing a shrink he'd be dead.
In addition, the psychiatrist on The Sopranos rarely had meaningful plotlines of her own (aside from her rape). She existed to further the character of Tony Soprano, not for her own sake. Deanna Troi, if TNG is ever rebooted, should exist as her own character, rather than serve as a tool to explore other characters.