Now in the PHB, a 50g potion is an item on the equipment list that costs less than a riding horse. Most people still won't have one. But it's primary purpose is to have healing when you're critically injured, or are away from civilization. I want the greater wilds and frontiers and untamed lands to be dangerous. Need to travel a long distance through dangerous terrain? That is when you want to have one.
Should point out that it's not merely the cost that matters, but the value, and the duration of that value.
When you get hurt, you
really, really want that healing potion. But how often do you get hurt? Or rather, how often do you get hurt badly enough that a healing potion becomes important, rather than just walking it off?
$5000 is a trip to the emergency room for something like a broken bone, or something needing stitches. It's something bad, but fixable. An average young person probably won't need to do that more than once every 10 years or so. And it's not uncommon even today for people to ignore problems and just hope they get better on their own, rather than deal with the cost of a hospital visit.
A horse, on the other hand, is something you will likely use every single day in a fantasy-like society. Whether it's a trip to town, carrying goods for sale, pulling a wagon, used by cowboys to manage their herds, or whatever else. It's like buying a car to drive to work every day.
Not having a car would be devastating for everything you do.
So you're willing to spend the money for the horse any time you don't have a horse because it's necessary and valuable over the long term. You're not willing to buy the healing potion when you may not ever need it — at least until you get bit and realize needing it and not having it is pretty bad.
So you save up for one, and then keep it locked away so you don't lose it, have it spilled or broken by rambunctious kids, have it stolen, or whatever else. And then 20 years later some adventurers come across an abandoned farm and find a small emergency stash with a healing potion and snatch it up for themselves.
So it's relatively easy to acquire, but not actually
needed that often. Price goes up a bit to reflect that only people who regularly get seriously hurt are going to regularly buy them.
This, however, is were we differ in preference. The concept of a "common" magic item should not exist. Personally, in a fantasy game, I don't like the magical equivalent to the modern conveniences we enjoy.
You're being disingenuous in conflating the mechanical term "Common" with the colloquial term "common", and treating them as if they mean the same thing.
And if we consider things in terms of "modern conveniences", there are more factors being ignored.
For example, using the conversion rate of $100 = 1 gp that seems a reasonable conversion rate, how many people go out and buy a new refrigerator? $1000-$2000 is 10-20 gp, what we'd consider a minor expense in-game, but that most people would consider a notable hit to the bank account. It's not exactly a casual purchase, even if it's doable. You need to check your budget before you decide.
But then scale up. You want to buy a new car. Almost everyone has a car. Let's say it costs $40,000, or 400 gp, the cost of an Uncommon magic item. But what's ignored is that almost nobody simply goes in and buys a car for $40,000. They get a loan, where they're paying a few hundred dollars a month over the course of years.
A few hundred dollars is a few gp per month. That's something on a scale that a person can afford. But going into a shop and buying an Uncommon magic item is like going into a car dealership and slapping the guy with a wad of cash to buy the car and drive it off the lot. People just don't have that kind of cash on hand, to make this a "casual" purchase. Adventurers do, but are clearly far from the norm.
And if you don't have a world with an economic system for loans and the like, you don't have a world where everyone on the street has magic items like that.
Even Common magic items are a bit of a stretch, given a cost of 100 gp/$10,000. You can save up for that, but given the power of Common magic items, people will really wonder whether you properly considered what else you could have spent that money on (such as a good horse).
I once took the 3E magic item creation rules, the GP limit by settlement rules, and the 3E spells to make a bunch of magic items that would revolutionize the world. A magic water pump could be made with Create Water for 1,000 gp, and it would spout two gallons of water every time someone pumped it (once every 6 seconds). It doesn't take that big of a town to pool together and get one (just make sure it's real heavy so it's hard to steal).
Heck, who's to say they haven't done just that? How do you make it unstealable? Basically turn it into a well — a huge stone construct buried into the ground. And a few hundred years later, nobody even remembers that it was a magic item, and not
actually a well.