That's true, though it's worth bearing in mind that if the player individually feels that their Barbarian is not capable of making decisions or acting in a certain way, it's still their right to play their character that way, and many still do ^.^ Berserker Barbarian has the post-rage fatigue build up that you remember - it comes into play when they use their frenzied rage, which grants them additional attacks. Exhaustion is (or can be) dangerously crippling in 5e, though, so it's a heavy cost-value decision that you make.
For spellcasting - one of the things that made spellcasters so grotesquely overpowered by even the mid levels, in older editions, was their ability to stack up various spell buffs and have them all running simultaneously. The solution to this was to limit buff-stacking substantially. A lot of folks react initially very badly to the concentration mechanic as it exists in 5e - especially if they're used to stacking up a dozen different wards and buffs and augments in advance before going into major fights - but in reality, it works out in a mostly balanced way and it's not as bad as many people's first takes are, when they come from older editions. It was also a necessary move, I have to say, like it or not (and I say that as someone who mainly plays casters and loves them... but full casters could break the world apart by tenth level, in older editions, and it wasn't great for everyone else). Even so, it's not perfect, and there are quite a number of spells that are concentration that don't really deserve to be, and a number of spells that are not concentration that probably should be.
First of all, yes - in 5e there are a lot of spells that now require concentration, and you can indeed only maintain concentration on one spell at a time. Doing other things does not endanger or interrupt that concentration - you can hold concentration on Storm Sphere and cast lightning bolt each subsequent turn without trouble, and you can use your reaction to counterspell someone without endangering your concentration. Only a few specific things break concentration, but casting another spell that requires concentration is one of them.
In most cases, however, your full spellcasters aren't going to have too much trouble juggling concentration in a fair and practical way. Choosing spells that synergise well, and not overloading your concentration spells versus your non concentration spells is just a part of picking your load out for a day, if you are a prepared caster. It IS a halter at times, and it's not perfect, but I'll stand by it being fundamentally necessary, coming off the spell stacking of older editions. Prebuffing for several minutes at the tabletop isn't fun or tactically interesting for anyone, really.
As a rule of thumb: If a spell deals damage, and can continue to deal damage each turn, then it will require concentration. If a spell buffs one or several party members above a certain grade of value, it will require concentration. If an effect crowd-controls or otherwise puts one or several targets out of action, or debilitates them for an on-going number of turns, it will generally require concentration to maintain the effect. If a spell summons one or several creatures, it will usually require concentration to keep them around and/or on your side. Outside of those factors, most spells will not require concentration, and balancing these is now part of the game of tactically picking your spells an when to cast which ones. Whether a particular effect is necessary or beneficial enough to be worth your concentration slot is a decision that most casters have to make now... and the balance is not always right; there are some spells that basically no-one will ever cast, because their effect simply isn't worth your concentration slot, and there are better options that are... and those are flaws in the system. Barksin is one such example - no sensible person will ever consider barkskin to be worth the concentration slot, and it realistically should be a spell, like mage armour, that does *not* take concentration.
Larian have, for the most part, followed the book when it comes to spells taking concentration or not - they've made a few silly moves, such as making mage hand concentration (it's not and shouldn't be), but overall they've followed things as written here. The major issue with concentration BG3 is that they have loaded on large amounts of incidental and unavoidable damage all over the place, which spams you with endless concentration checks - so you will fail one and lose your concentration far, far FAR more easily in BG3 than you would in a normal 5e game.
They've also got bad stacking on some of their status conditions which cause automatic concentration losses that should not happen (being knocked prone causes automatic, no save, concentration loss in BG3 - when it does not do so in normal 5e; this is because in Larian's game, 'prone' also applies 'unconscious' for some ridiculous reason, so any time you fall down, you are also temporarily 'unconscious' and your concentration breaks. It's been reported since the early days of the EA, with no change ever happening.
Here's an example: You have a concentration spell up - suppose you're holding call lightning so you can zap several targets heavily each turn with a single spell slot. A goblin over the other side of the camp runs 30 feet, uses its bonus action dash to run 30 more feet and now has line of sight on you, despite you tucking yourself away as best you could - the maps are too small to actually get 'safe' in this regard. The goblin uses its action to fire an arrow of roaring thunder at you; it rolls a natural 1 and misses... BUT, the arrow still lands on the space it shot at, your space, and so when it explodes it still blasts you backwards 10 feet; you pass this save and take only 2 points of thunder damage, but you still get thrown, and you still fall prone, and so your concentration still automatically ends. There was nothing you could have done about any of that, in Larian's game - you couldn't stay out of LoS from the goblin, the goblin missed, you passed the save you shouldn't have had to make... you still lose concentration, without so much as a save to keep it. They are making the game extremely concentration unfriendly.
Along with this, they've also made numerous concentration spells much weaker or limited - either by shortening their durations, or by not letting you pick the targets of them like you're supposed to be able to (it is on record in bug reports as being their intention that you cannot chose which two targets your would try to affect on an upcast hold person - you just highlight a point and hope it hits the two creatures you want, which is utterly ridiculous...), or by making the effects caused by them easy to remove or dispel by any character in ways they should not be (You put down a stinking cloud to cover an area and stop creatures getting to your party; a goblin throws a candle from the table at the cloud, it explodes in fire and then is gone. The other goblins all run through unimpeded. Elsewhere you cast an incendiary cloud to melt a mass of enemies. Next turn, the goblin priestess casts darkness on the same space, and her darkness spell displaces and removes yours, because Larian's engine can only handle one effect in a place at a time - and the AI Knows and abuses this!). Overall, while Larian have stuck mostly to what is and isn't concentration, they've also made the concentration mechanic itself seem and feel much more crippling and unfriendly than it should be, by way of their other design decisions.
I suspect I'm not going to sell you on it regardless, and that's okay - but those are the reasons.
