Li Shenron
Legend
You are absolutely right on all accounts.A jack of all trades character class has never been good design in a team RPG, and this is due to the fact that you can only do one thing at once so the definition of the concept is that you are always doing something you aren't the best at.
It works in a solo/team cRPG because the PCs in most CRPGs are Special and surrounded by NPCs who are, ultimately, not as good at things as they are. If you take, for example, a reasonably skilled player playing as Commander Shepherd your guns are probably doing more damage than those of your squadmates no matter which class you pick assuming you care enough about shooting to use them at all. Because, being a PC surrounded by NPCs you are awesome - your choice is how to be awesome and "I'm awesome because I'm as good as anyone at anything" works.
But in a team based RPG your team mates are masters of things. A Jack Of All Trades Master of None can only do one thing at once so they are never ever doing anything they are a master at. They are always second rate compared to other party members. And they can't even do everything at once, stacking synergies, due to the action economy and due to that being something they would be a master at.
In D&D 5e it is worse than that because there are a number of hybrid characters with secondary areas. A paladin, for example, is a primary brawler and secondary healer and secondary face. By contrast a melee cleric is a primary healer and secondary brawler. A "jack of all trades" brawls like a cleric and heals like a paladin. And stealths at best like a non-Shadow monk, but not like a rogue, ranger, or shadow monk.
So given that most characters are flexible and should be able to contribute in all three pillars (meaning they should have at least three areas of reasonable expertise of which a non-JOAT class should be a master of at least one) you're down to at least the fourth and probably the fifth or sixth area a class contributes in before a Jack of All Trades nature means that its area of all trades is better than the mediocrity of another class unless they are actually a master of something, exploiting synergies.
A roleplay game is about each PC having a role, it's ok that complex RPGs like D&D allow everyone to have secondary roles, but if someone has too many roles then inevitably the whole character is diluted down. My personal opinion is that JOAT characters are made for 2 kinds of players, those who genuinely can't decide what to play, and those who want to win the game against the others. For the first kind, it is better to just remind them that they are not going to have only a single shot at playing the game in their entire life, they can play one character role in this campaign and another role in the next.