The premise of the game will vary by table. Not all games are about groups of mighty adventurers. That may be a kind of default assumption, but it's far from universal.
Or the default assumption might be closer to pragmatic spell-casting treasure-hunters...
..or murder hobos. ;P
Not all characters are meant to be "equal members of a serious adventuring party".
Any that are members of a serious adventuring party, expecting to be treated equally, should probably strive to be close.
There are other ways for a character to be effective than just the narrow focus typically attributed by class.
Class can be problematic, that way. A fighter can focus on being a great diplomat, but he will give up more of his effectiveness to achieve less capability as a diplomat than, say, a Rogue, Sorcerer, or Paladin.
I summon [MENTION=996]Tony Vargas[/MENTION] to read your post (if he hasn't already) and agree with you, as presenting one particular application of the general doctrine that, in 5e, the GM is fully in charge of the game and its outcomes.
Effing pentagrams...
It's not that the obstacles are illusionary, but the idea that there are specific obstacles that must be overcome in a specific way is the illusion. The obstacles depend on the PCs. If the players have different characters you just have different obstacles, not that the players fail somehow.
A DM is entirely within his rights to do that, of course, in any system. And, in 5e, particularly, is Empowered to do so, and backed up/encouraged by a system that refers back to him for the method of resolution of every action...
For example, all other things being equal a STR 8 Fighter has a 20% chance less of hitting something than a STR 15 Fighter. ...
And all other things are not equal. The STR 8 fighter (if using the standard array, anyway) has a 15 Ability somewhere else, so she's got a better chance of overcoming some other obstacle using that Ability, which might sometimes totally eliminate the need for the combat at all, or resolve the combat some other way than just hitting things.
True enough in theory, but going that way hardly leverages the class features of the fighter, now does it? It might be very true to concept, and even kinda philosophically deep, ("The greatest warrior is the one who does not need to fight at all"), but the system punishes you for going there with dis-synergy.
In addition, the DM isn't meant to be a robot who pushes out the same encounters regardless of the PCs capabilities. The DMG talks a lot about scaling encounters and so forth to the capabilities of the PCs. So the weaker fighter might not be fighting the same opponent, or the same number of opponents, etc.
Encounter design and encounter/day guidelines are just that, guidelines, and the DM is entirely free to color far outside them. The only way to be sure to challenge the party is to challenge the /party/, not the typical of their level, because there's just too much variability in what a party of a given level might be able to do in 5e, among considerations like player skill, DM style, class composition, optional rules in play and/or presence of magic items. Similarly, the only way to ensure balance among the members of that party it to tailor challenges to highlight each of them at various times.
It's not just fights, either....
This is very table-dependent. ...
And at least some tables use "objective" rather than "subjective" DCs, which means that if the gameworld is a certain way, PCs with low bonuses will be objectively more likely to fail.
Meh, the DM decides what the gameworld is like, so there is no 'if the game world is a certain way,' the game world is the certain way the DM decided upon, and he can make - or amend - that decision, at any point before revealing it to the players (and quite possibly, after, with a bit of hand-waving and plausible deniability).
(The only edition of D&D to officially use "subjective" DCs is 4e, but it sets these by level, not by character ability - contrast, say, HeroQuest revised - and so even there you'll have more failure with weaker PCs.)
Those are not subjective DCs, but challenge-by-level guidelines.
5e, though, leaves the DM freedom to make success/failure or DCs as subjective as suits his style. In fact, doing so can be a good idea, as it lets you compensate for the lack of substantial numeric advancement that can be a source of consternation to players. The DM is free to narrate success when the 18 STR fighter kicks a door in, call for a DC 15 roll from the 14 STR cleric, and rule the 8 STR wizard automatically fails. If the DC were simply 15 for all of them, the fighter would (inappropriately) fail half the time, and the wizard might as well take a quick shot at it before breaking out a Knock, because he might roll high.
