It's funny you surround 'according to the rulebook' with all these qualifiers like it's some sort of thing you think should be ignored by it being too strict, or too odd to consider. As if it's unfair.
It's a rule book. Rules are strict. That's what they do, they restrict.
Not at all. As I have stated, we practice even more restrictive rulings regarding what goes in our gaming table around here. Nothing unfair or badwrongfun in that.
Player's Handbook, Page 163
Chapter 6: Customization Options
Multiclassing and Feats:
"Your DM decides whether these options are available in a campaign."
The thing is, the same way a DM can decide that feats and multiclassing are in or out, or that in their campaign only a handful of feats are available, or that some specific multiclass combination is out, they can also decide that access to the raise dead spell is restricted to clerics of life and death deities, or that elves don't exist in their homebrew, or whatever. That there is no labeling on these other game options hasn't prevented gaming tables around from doing just that.
In 5E (or GURPS), we don't have to guess, because the books tell us what part of the game is essential to the core and which parts are designed to be optional. In 5E, at least, there are two different parameters by which something may or may not be allowed - some things are not considered to be optional (without getting into house rule territory), but some things are both optional and assumed to be included. They actually go over this whole topic... somewhere... probably in the DMG.
This is the intent of the designers, which they have codified in the rulebook. In theory, that means we should all be on the same page about this, and anyone who assumes feats by default is being a self-entitled jerk. In practice, it operates a lot more like an echo chamber: players use the options they want, and play with others who use those options, so their personal experience teaches them that those options are considered normal, and they very reasonably expect those options by default. It's a type of cognitive bias for which few people practice compensating.
- Feats are optional and unassumed. Never bring a character with feats to an unknown game unless the DM specifically tells you that this option is in effect. Even then, individual feats are still optional, and can be included or discluded by the DM (or setting designer) as they see fit.
- Multiclassing is optional and unassumed, as with feats. The DM has every right to say that paladin/warlock is specifically disallowed, if that makes sense for their setting.
- The class construct is not considered optional. Every single class in the game is individually optional, but assumed. Unless the DM (or setting designer) specifically says otherwise, you can probably play a monk or warlock or whatever.
- The race construct is not considered optional. Each individual race is optional, but only the common races are necessarily assumed. If you want to play a gnome or half-orc, you should ask first. Regardless, any specific race may be disallowed by the DM (or setting designer).
- The background construct appears to be optional, but assumed. You don't have to pick a background, but if you don't, then you still have to pick the features that would otherwise come from your background.
It seems to me more of a marketing strategy (which, of course, is part of game designing) decision than a "system engine" design decision to label some non-essential elements of the game as optional but not others. And I point Adventurers League as evidence, as there, the optional and unassumed feats are actually legal. I could even say that getting rid of racial penalties to ability scores, or that the average range of ability scores giving positive modifiers are a marketing strategy too.
Let me clarify my position. If a set of (non-essential) rules are likely to turn off a part of the gaming community, but suppressing these rules could upset other part of this same community, just label them as optional. Folks who like these options will add them and never care about the label, but folks who dislike don't need to do anything in the game. This is exactly the same, to me at least, as to present these same rules without any label, and letting the folks who dislike them to ban these options (as I already do with a lot of other options in the game), but for somebody else, the first scenario might feel more comfortable, as it avoids the negative of subtracting something from the game.
Similarly with ability scores, if PCs had smaller numbers (from, say, smaller racial bonuses or even because of racial penalties, and resulting in overall smaller modifiers that go deeper into negative territory) and monsters had proportionally smaller numbers, the game could be exactly the same. After all, the difference between a -2 modifier and a -1 modifier is the same as the difference between a +1 and a +2. But negatives seem to upset people, so just adjusting the whole baseline mathematics of the game up (by making positive modifiers more common but also inflating monster HPs, for instance) seems to make everybody happier.
Oh, and I am not criticizing any of those design decisions, it seems they work quite cleverly from a marketing standpoint while not really affecting gaming experience in any significant way.