There are so many things wrong with these examples it's hard to know where to start.
Again, you're stuck in the false assumption that you're limited to the mechanics on your character sheet and nothing else.
Let me try to give some real world examples. I'll change some of the details so we don't get hung up on a specific system.
Example 1: The Tough Opponent
You're a spellcaster and your spells cannot affect a magic resistant creature. Or you don't have the right magic weapon to get past the Damage Reduction (or you're just not strong enough to do enough damage).
What can your character realistically do during this fight? Maybe you can get into a position to flank the monster to give the ally better odds to hit? (Or trip the monster? Or temporarily blind it?) More than likely the enemy is too dangerous for you to get close enough to it. Or it's too strong to be tripped. And your trying to get close enough to do something/anything is just going to put you in danger and it's a smarter decision to let the tank be the tank.
And how long does this fight take ... maybe 30-40 minutes? How often do these battles come up where you can do nothing ... maybe once or twice a session?
You're assuming that you have to hit the target where it's strongest and since that doesn't work, you throw up your hands and quit. It's an odd reaction.
This is where creativity in general and creativity specifically with spells comes into play. The old standbys of casting
rock to mud on the ground and letting the tough opponent sink into the mud...only to cancel or cast the reverse spell,
mud to rock, thereby trapping the opponent in the rock and making them an easier target. Or casting
wall of stone above the target's head and letting gravity do its thing. You don't have to attack the target directly. That's a choice you're making. And you certainly don't have to attack the target where they're strongest. If they're magic resistant, don't attack them directly with magic. You're a spellcaster, okay...so? Don't attack them directly with magic. Attack them indirectly with magic or directly with non-magical means. Don't have a staff, dagger, sling, crossbow, etc? That was a mistake on your part. Don't have utility spells that can effect the environment? That was a mistake on your part. If nothing else, pick up a rock from the ground and throw it.
Example 2: Shut Your Mouth, Barbarian
The party needs to infiltrate the royal ball and make an important deal with a noble. Your barbarian has no training in a useful social skill - even if she has Intimidate, that's a bad idea in the circumstances. The spotlight is on the bard who can wheel and deal through intense roleplaying scenes that last about an hour. In the meanwhile, the barbarian does nothing. Now imagine a campaign that has a lot of these moments, 2-3 scenes per session (on average). Now you still need the muscle of the barbarian in the party for when things go bad, but for the most part, you're sitting there doing nothing.
Again, several things being overlooked. There's all the prelude to this scene. You're a group of adventurers who're trying to infiltrate the royal ball...okay. So what was the barbarian doing during the hours of planning and setup? Chances are they could contribute a lot during that. Gather information, intimidate kitchen staff, etc. During this scene there's always the distraction angle, replacing one of the guards, replacing one of the kitchen staff, pretending to be a temp hire, etc. Pick an episode of Leverage and watch that. Watch what the character Eliot Spencer does and take notes. Pass those along to the barbarian's player.
Example 3: I Just Need to Sneak
The rogue with his high Dexterity, light armor, and great Stealth check doesn't want the clumsy wizard following or the racket of the paladin in full plate. It's important to get the layout of the bandit keep, and the rogue has a good disguise if he gets spied anyway. It just isn't believable for the wizard to come along. I guess we should all go grab a beer for 45 minutes?
If you intentionally exclude every way the wizard can make that scouting mission easier or completely obviate it, sure. All the charm spells, all the divination spells, all the transmutation spells, polymorph, invisibility, portable holes, bags of holding, etc. If you decide ahead of time that the only useful thing is a Dexterity (Stealth) check, then sure...having a high Dexterity and expertise in Stealth wins the day. But you're intentionally ignoring about 1/4 of the wizard's spell list to get there.
Example 4: The Know-It All vs. the Specialist
Hey, it's really important for the good of the party that you're an expert in healing and medicine. After all, it's important that characters get to live. So you max out ranks in healing, purchase good medical equipment to keep the party alive. But what you don't have - effective weapons or combat abilities. Skill ranks in persuasion or knowledge about politics. Maybe you can create a sedative to use on the enemy to help bolster the party? No, it doesn't work that way? Okay. You're essentially an NPC at this point. That other guy - the guy who got to take all the knowledge skills and can interact with roleplay and combat - that's the hero and you're just making it so he can have fun. The minute you dare open your mouth with your Charisma penalties, you've doomed the party to failure, you selfish jerk.
Yes, going out of your way to make a pacifist healer in a game about fighting monsters means you're not going to be as effective in combat. That's a character "build" problem. It's also worth noting that this isn't how D&D has actually worked since 3E. There are no ranks in skills. Haven't been since about 2008. In both 4E and 5E you have to work really, really hard to make a character who's not effective in combat.
A big note here: having social skills is not required to roleplay. You can roleplay with terrible social skills.
I think a secondary problem is you might be doing the "if it's not perfect, it sucks" thing where you decide ahead of time that only the character with the best stat+skill combo is
allowed to make the check. That's not a game problem. That's a player mentality problem.
I hope these 4 Examples - which are ones I see almost weekly - illustrate how many RPGs do a poor job of maintaining fun for the majority of players throughout the session. I think your players would agree, if you asked them. For a hobby that purports to be cooperative, it really rewards solo design.
If you're seeing these weekly you need a new group and definitely a new referee. This is also one of the major reasons I play old-school games or extremely rules light games, they tend to bring out player creativity, lateral thinking, and puzzle solving.
There's also a bit of "always needing the spotlight" going on. The other characters get to shine, too. Not every character is going to be the star of every scene. If the referee is lingering on some character's spotlight time while glossing over others' spotlight time, that's a referee problem.
