All too often, this is the missing piece of context that detractors of early D&D fail to understand.
Nowadays, the norm is that you play the character you want to play because that's your character, the singular protagonist of your singular story, and just like a protagonist of written fiction, there need not be any limits on who or what can reasonably be the protagonist of your story.
In early D&D, the milieu has priority over the characters. Ability score requirements are there to make the sub-classes rare, and racial class restrictions and level limits are there to enforce the genre (human-centric sword & sorcery). Add to that the fact that the fighter sub-classes were all basically fighters but better, and you especially needed for the paladins and rangers (and, I guess, barbarians and cavaliers if you were a heretic) to be gate-kept to make the common fighters, well, common.
Unearthed Arcana looks positively insane to someone like myself, who came into the hobby during the 2nd edition days, when Zeb walked back a lot of the excesses of 1st edition: scores rolled on straight ironman 3d6 in order (without even the option to adjust stats 2-for-1 like in Basic), the sub-classes all clearly marked in the PHB as campaign-optional and pending DM approval, constant exhortation in the text of 2e to prefer low stats over high and weak characters over strong because that was a mark of "good roleplaying", etc., etc. But even 2e kept up the notion of a human-centric milieu and the fact that most PCs should be human fighters, mages, clerics, and thieves—because that kept sub-classes like paladins, rangers, bards, druids, and specialist wizards relatively rare and therefore special when you managed to qualify for them. And that was something that we've lost along the way! The 2nd edition DMG warns that if you make a campaign-specific rule that gnomes can now be paladins, don't be surprised when your campaign is overrun by gnome paladins! (A sentiment which makes perfect sense in a game where gnomes have special abilities that humans don't, and paladins have special abilities that fighters don't.)
From 3rd edition forward, the desire to center the player character as the focus of the campaign (which clearly most groups were already doing; 3e was nothing if not a response to the market demand of its day) led to a removal of all such restrictions and limits, but also a leveling of options—from then forward, humans had to be on par with all the other races in terms of advantages, and fighters had to be on par with all other classes. While the success of this endeavor has varied since 2000 (I don't think anybody would argue with the contention that the 3.0 martial types, the ranger especially, were all pretty terrible in terms of balance against the caster types), it has also resulted in a markedly different sort of game, and one that doesn't really support the same style of troupe play that really sings when you play one of the TSR editions in that style. But more notably, nobody who plays a WotC edition would ever argue that paladins and rangers are something special in the way they (ostensibly) were during the TSR era.
In the old days, having a special character was at least in theory supposed to be a rarity. Now it's the norm, and so The Incredibles maxim holds demonstrably true: when everyone is special no one is.