Dwarves, elves, and halflings as a class really only make some amount of sense in the context of an introductory beginners game. It's easier to get new people actually playing quickly.
When BECMI became its own game line, continuing with that really did get weird.
Amusingly, the original Holmes Basic set, the only one which was purely an introductory beginners' game, still had separate race & class, as it was an adaptation of OD&D, in which they were originally separate (although demihumans didn't have a lot of options).
Race as class was first introduced in the 1981 Moldvay Basic & Cook Expert, then continued in 1983's Mentzer BECM series. Apparently part of the intent was indeed to be simpler for new young players, but part of it was also that B/X was prompted by one of the Arneson lawsuits over royalties on AD&D 1E, and TSR wanted to make the "Dungeons & Dragons" game more distinct from Advanced Dungeons & Dragons.
I assume it stemmed from the intended milieu. The assumed setting was one focused primarily on humans, living in human lands, interacting with other humans. Most people would never meet a demihuman, but maybe you’d have a cousin who swears he saw an elf in the woods once, or a grandpa who everyone loves to hear tell the story of the time a company of dwarves passed through the village when he was a young boy. In that context, the demihumans a PC is likely to encounter are disproportionately likely to be adventurers, and there’s not a whole lot of need to model much variety in their culture.
Of course, naturally this isn’t going to be the sort of milieu every group wants to play in (and with the benefit of hindsight we can see that more cosmopolitan milieus tend to be more popular), so it seems only natural that demand for a race/class divide would emerge before long.
Right, I think this is the approach most people who enjoy race as class take. The idea is that demi-humans are DIFFERENT. They operate by different rules and don't do all the same stuff humans do, and this mechanizes part of the setting. I'm generally a fan of this approach, though I still enjoy games that have them separate.
Given the ease of designing racial classes in the B/X framework, you can also flesh them out with more options if you want to. Adventurer, Conqueror, King takes this approach in building on B/X, giving demihumans more options without making them the same as the human classes.
If you are doing one shot low level D&D or a low level campaign then they are fairly fantastic from a power perspective. An elven fighter magic-user or a BX elf is pretty much mechanically superior in every way to a level 1 magic user for a one shot adventure.
If you are doing a high level one shot game or a game that expects to get to high levels beyond the level caps they become poor choices in a power sense. a 4th or 6th level cap puts you really far behind the expected power curve in a 15th level module with your fellow PCs at 15th level and monsters tuned for that level of challenge and threat.
Thankfully the level caps are significantly higher in B/X than they are in OD&D. In B/X Halflings cap out the lowest at 8th, Elves at 10th and Dwarves at 12th, which isn't too bad when the max level in the game is 14th.
Definitely one thing I think is neat about the racial classes in B/X is just being able to have elves pay more xp for being a straight up fighter/mage with some extra abilities. Elves ARE badass. But taking the same amount of xp to hit 2nd level as the Fighter needs to hit 3rd is a cost. My most successful OSE character from my online play during the pandemic has been a Half Elf from advanced OSE. He has notably inferior spellcasting compared to a full Elf, but advances faster. There are multiple times I've rued that (and not having the immunity to ghoul paralysis!), but OTOH, there have also been multiple encounters where I would have died if I was lower level, due to having fewer HP.
If you're doing a one-shot with characters starting above 1st level in pre-WotC editions, you always want to specify the number of xp rather than the level for characters to be generated. If you specify 20,000, for example, your Magic Users will be 5th level, but your Elves will still be 4th.
I don’t get that vibe from race as class necessarily, but I definitely get it from the level limits that you got once race and class split off from each other.
Personally, what I would love to see in an old school styled game is a situation where your choice of race determines what you roll to determine your abilities. Kind of a reversal of racial ability requirements - instead of being unable to play an elf because you only rolled 7 intelligence, you might choose to play an elf because you want to play a high-intelligence character and elves have a better chance of that.
For example, imagine if humans roll 4d6 drop lowest for each ability (in order), whereas demihumans roll 3d6 for most abilities and 2d6+6 for two of their abilities (also in order). So if you specifically want to play a certain class, picking a race that compliments it will give you a better chance of getting high stats in its prime requisites, at the risk of a greater standard deviation in other abilities. Whereas human becomes the go-to if you don’t have a specific class in mind and just want to play whatever you roll the stats for.
5 Torches Deep does this. If you're human it has you roll 3d6 in order, but you can swap two. Demi-humans get a fixed above-average value for their main ability scores, and roll others on 2d6+3.