First, I'm not looking at the MM for racial bonuses. Second, balance plays a part in things, too. WotC has many rules that don't make complete sense until you factor in balance. That the PCs get a lower bonus than the MM version due to balance does not negate what I am saying. You don't get to say, "But the MM version is even more dexterous than the PC version, so therefore PCs should get a dex bonus, and the dex bonus they get didn't come from their race as a whole."
Let's look at Aarakocra. The MM race has a very high dex as a race. The PCs get +2 dex. Their next highest stat is wisdom. They get +1 wisdom as PCs. The racial bonuses for PCs match the racial advantages of their race. I'm sure if I examined the other "exceptions" you mention, I will find them to be similar.
So lets thought experiment that...
First off, I'm disqualifying Satyr, Minotaur, and Centaur; they come from M:TG books and its very easy to say "but that's the Magic version of them, not the D&D one) so off they go. Second, to qualify it has to be the "X" as a monster, no variants. (so "hobgoblin" counts, but "tabaxi minstrel" doesn't). Lastly, we'll assume a base score of 10 or 11, whichever seems more applicable.
Aarakroca - MM gets +4 Dex, +1 Wis, ability to summon an air elemental when with 4 other non-PC Aarakroca (a PC and four monstrous aarakroca apparently doesn't qualify)
Bugbear: +4 Str, +4 Dex, +2 Con (-2 Int, -1 Cha), has brute (extra wpn damage), lacks powerful build and long limbed. Apparently, MM bugbears have stubby limbs.
Changling: Monster version has -2 Str, +4 Dex, +1 Con, +4 Int, +6 Cha (PC has +2 Cha, +1 any) and has unsettling visage (which PC versions once got in the playtest). Monstrous ones can appear as scary, but PCs cannot.
Duergar: MM +4 str, +4 Con. Surprisingly close on the remainder, assuming the MM version is effectively equivalent a "5th level" character...
Drow: +4 Dex, +1 Cha. Same as Duergar.
Gnome: Svirfneblin: +4 Str, +4 Dex, +4 Con, +1(!) Int, -1 Cha. Not even close to the +2 Int, +1 Dex of the PC. Also, the MM version is equal to a 4th level PC who took the Gnome Deep Magic feat.
Goblin: +4 Dex, but -2 to Str, Int, and Cha. (The PC race makes out better on this with +1 con). Apparently, MM goblins lack anger management issues, as they don't have Fury of the Small the PCs do. (Maybe they become adventurers due to all that pent up aggression).
Hobgoblin: +2 Str, +1 Dex, +1 Con (vs the PCs, +2 Con, +1 INT?!). MM hobgoblins get extra damage with allies (martial advantage) but are less obsessed with appearance (no saving face).
Kalshatar: +1 Str, +4 dex, +1 Con, +2 Int, +4 Wis, +4 Cha (vs the PCs +2 Wis, +1 Cha). Everything else looks the same.
Kenku: +6 dex, that's it. MM kenku though are excellent ambushers, something PC ones lack.
Kobold: +4 dex (the rest are below 10). I at least the PC ones are consistent. Of course, the PC ones can Grovel, Cower and Beg; something their MM brethren never learned. (Maybe PCs used it first on WotC to get better ability scores?)
Lizardfolk: +4 Str, +2 Con, +1 Wis (penalty to Int/Cha). The artisan lizardfolk are the adventurers since PCs can all craft simple weapons and shields, and they also are the hungier ones since they get temp hp for biting. That said, the regular lizardfolk learned how to bite and swing a weapon at the same time...
Orc +6 Str, +1 Dex, +6 Con, (Int penalty). Well, the old Volo one as fairly accurate, and the newer one better. Of course, the MM lacks powerful build as well.
Shifter: the monstrous one is a longtooth (bite attack) so we'll use that subrace. +1 Str, +6 Dex, +4 Con, +4 Wis. Based on the formula (lvl + con) for shifting, all monstrous Shifters are 3rd level.
Tortle: +4 Str, +1 Con +2 Wis, +1 Cha. Fairly close otherwise.
Yuan-ti Pureblood: +1 Dex, +2 Int, +4 Cha. A monstrous YTP can only use the poison spray cantrip 3/day (vs the PC using it infinitely) but of course, the MM has multi-attack to more than make up for it.
So, some races I agree with you; they are close. Some are wildly off not just by how much but what scores are bumped. As for the remaining "racial" traits, it's a toss-up; some races have abilities PCs never get, and some PCs have racial traits their NPC brethren never get. I think it supports my point though; the PC stats aren't supposed to be "representative" of the race in general, but instead a collection of abilities that the player will find useful without being overpowering. You simply cannot assume that since the PC race "gets" a specific trait, its universal for all members of that race.