See, I think the sticking point is "reasonably popular". To me, they just aren't. They aren't played that much (and I suspect that the amount is shrinking by percentage daily) and never have been. They don't appear in adventures and barely appear in setting guides. Take a guess how many times the word halfling appears in the 5e DMG?
Dragonborn are mentioned twice, and they're supposedly a lot more popular than halflings are.
The number of times they're mentioned in the DMG or a published adventure isn't indicative of how popular they are as PCs--just that they're not often used as NPCs.
Also, you don't know that they're not played that much. They're not common on D&D Beyond, which many, even most, players don't use.
Folks keep talking about how we dislike halflings. I certainly don't. What's to dislike? Something would have to actually appear anywhere in the game to engender some sort of feeling.
But instead of shrugging and moving on, you are certainly spilling a lot of electrons in talking about how they should be removed from the PH. And it's not like the presence of halflings is actually hurting anyone, nor is there any reason to believe that their presence is keeping other races out for a future edition. I could understand you complaining about halflings if they were actually causing some sort of legitimate problem, but they're not.
I would say that both Dragonborn and Tielfings have certainly "earned" their inclusion. They are two of the most commonly played races in the game according to the information we have.
I looked up what I could find about dragonborn lore and... much of it makes them very much like scaly dwarfs: honorable, clan-based, crafters with a preference for metal and jewels, traditionally more martial than magical. The primary difference is that they're also highly emotional and don't seem to have any particular love of ale, beards, or axes. They're interesting as a substitute for dwarfs, but it also seems like a lot of people don't like them because their traits are weak.
It's half-orc, gnome and halfling that have been included mostly for nostalgia reasons and nothing else. If you play a halfling in a WotC game - presuming the DM is using a WotC adventure - odds are you will be the only halfling in that entire campaign.
You've already said you have nothing to back this up, so you should probably stop making this claim.
Also, lots of people don't use published adventures, or make radical changes to fit them into their own world rather than whatever world (Realms) they're set it.
There will be no halfling NPC's, no halfling references, nothing. You might as well be playing a goblin or a tabaxi for all the connection your lineage choice will have to the adventure you are playing.
And? Is it common for people to play adventures using only the races mentioned in the published adventure? The Icewind Dale game I'm in has a leonin, a tabaxi, a firbolg, a gnome, a changeling, and a gith (can't remember if he's a 'yanki or 'zerai). I have a feeling that party compilations like this are just as common, or maybe even more so, than parties where everyone has some intrinsic connection to the area.
Also, I own two adventures: CoS and ToA. In both of them, the PCs are supposed to be whisked away from their native land and dropped into the adventure, meaning that having a native PC with any sort of connection to the area is not considered to be an option for those adventures.
And finally, it's been said, frequently, that many halflings live among humans, so if there's a human population in the area, there will be halflings. Maybe they're not directly mentioned by the adventure, but they're there in the background.
