Without knowing what particular house rule you were playing with, I'd say it's not really a different set-up from 3.5E D&D. Presumably in your game, you could still have a character who is strong and invulnerable, and only strong and invulnerable (spending all of your points on stuff like flash defense, power defense, various advantages to Strength, etc.). But the players in your party chose not to.In effect, you all chose to be "clerics" or "wizards" or "eldritch knights" instead of straight "fighters", for instance.
You can find the houserules on the IMO forum if you dig, but rather than discuss them now, let's go with your suggestion and look at how a how a dude who is just "Strong and Invulnerable" interacts with that encounter. Despite being a two-trick pony, there are still 2 or 3 of the objectives that a character who is "Strong and Invulnerable" can contribute to.
Obviously he participates in the "beat up the pirates" slugfest with superstrength. And while maybe not ideal for the job, he's passable as a distraction by using a feat of strength to draw attention and invulnerability to soak gunfire and he can also be a failsafe if the party fails the "calm Cap'n Kraken" objective as he uses his invulnerability to soak the attacks of the monster.
So that whole encounter is set up such that even characters with limited areas of competence have multiple ways to participate meaningfully.
To contrast: more straightforward encounters with fewer and narrower objectives are more likely to lead to situations where characters with narrow areas of competence are less likely to be able to participate. StrongToughOnly Guy does fine in a straightforward punch-em-up, but needs help if there's a followup encounter where " now you have catch up to the fleeing pirates in their speedboat" and he is an outright detriment if the initial encounter is set to "the PCs MUST sneak in and free the hostages first, because if anything at all fishy happens the bad guys just start shooting folks"
To further contrast: higher difficulty encounters are more likely to
require
the correct type of specialist. If say it's not a sinking yacht, but is instead navy ship with a damaged reactor, you NEED to have StrongToughOnly Guy's immunity to radiation, and If say the pirates all have cloaking devices or magical rings of invisibility then you NEED to have someone who can See or Dispel Invisible
And that's why I'm having trouble evaluating 4e-style ROLEs independent from other game considerations
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