You’re assuming that the left- and right-handed handles are rotationally symmetrical around the vertical axis. The door handles in my home are not. As it happens, mine are symmetrical on the longitudinal axis, but they don’t have to be.
I see what you’re saying, turn them over heads-to tails like flipping a playing card instead of rotating them from three o’ clock to nine. I had to do some experiments with my stapler. I think our disconnect is we’re talking about two different things, moving a handle from the right side of a door to the left side, which really means getting a door that goes the other way, and replacing a doorknob on the same side.
Okay, say you have a door. As you’re facing it, the doorknob is on your right. You need to replace the doorknob. If you replace it with the handle type, it has to be one where the handle points to the left; if you have one that points to the right and rotate it around the up-down axis like you say, it just plain goes the wrong way. If you rotate it from 3 to 9, it works, but it’s upside down. The thing about the round ones is you can rotate them both ways and the still will work.
Via arithmetic, you arrived at the same conclusion as me. (Remind me of the total area of the EU? 
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If the same sales are to be split between two versions, there’s no difference to stocking double the quantity of the single version.
As I see it, the main reason is fashion and habit. Fashion can be explained by people who understand it…habit, however, explains why American light switches work the wrong way 
There’s no ‘correct’ way to fit a light switch, and given that we’ve found no great reason for circular door fastenings along with some reasons against them, can we put this answer down to ‘what people expect’?
No, I’m assuming the handle on one side of the door is a mirror image of the handle on the other side of the door.
Look, I drew a picture. Is there something about your door handles I’m missing?
I ripped out the pocket on an expensive suit jacket that way.
Old homes have beautiful glass doorknobs, sometimes in lovely colors. I have never seen a door handle as pretty as an antique doorknob.
No - apparently the manufacture of mirror-image versions is prohibitively expensive
Look harder. I’ve never seen a beautiful glass doorknob, only garish things which had little reason to exist.
You’re assuming that any shape can be rotated into its mirror image.
No, I’m not. But, while this issue is almost as important a subject as the definition of a pancake (something I’ve actually argued about with a friend once), it is time for me to go to bed. G’night :).
Hey, you’re the one who said big without proscribing the type of bigularity. The UK would fit in the western half of my state almost as-is, so the UK doesn’t have the kind of geographical bignessness we get over in these parts. Number of people, now, that’s a biguity of a different horse.
And hey, by the way, how much of the EU does use that weird metric door stuff you got over there? I mean, if you’re gonna embiggen your bigness, you gotta demonstrate them doorknobs are in use throughout the EU, don’tcha? Not that I can demonstrate that roundy-knobs are universal in the U.S. as the OP alleges; most public places either have panic bars or door handles.
Still, with the bigulated land area and population the US covers with one common language, there may be more at work than fashion or inertia. I’m not talking about uniformity of building codes, I’m talking about something even more influential: lobbyists. Maybe there’s a powerful Doorknob Cartel out there who once wined and dined President Coolidge with promises of sultry doorknobs if he just signed their prostitute bill. Or something.
I love those old glass doorknobs, especially the colored ones!
Here in the US to comply with the Americans with Disabilities Act, all commercial buildings must have handles.
When I moved into a new office this year, the contractor had to change out 6 doorknob locksets to door handle sets so my building would be compliant with ADA.
So unless the OP is staying in a hotel that is not ADA compliant, chances are the knobs they saw were in private homes.
Antique doorknobs are beautiful: brass, glass, or porcelain. Unless you have an elderly or disabled person in your household, why would you want a door handle?
There is one advantage to door handles that no one’s mentioned yet, they make it impossible to get hit on the ass with the doorknob on the way out. There is no doorknob!
So you can open the door with your foot when your arms are full. It’s good balancing practice.
Unless my eyes just skipped over it, nobody has pointed out that they are, in fact, fairly common here. At Home Depot, side by side with all of the door knobs are their door handle brethren. Every time I have replaced a door in my house (a 45+ year old home with aging doors and hardware), I have replaced the hardware with beautiful curved door handles.
Aside from the occasional ripped pocket, I really like the feel of the curved brass under my hand as I the weight of my hand opens the door – no gripping and twisting needed.
By the way, the second handle in the OP is upside down. That bugs me when I see them mounted like that. The main curved part should be facing upward, like on these since it feels nicer in the hand.
Catching things on door handles is so out-of-date. Door handles can easily be made so that things won’t catch. Just bend the handle down to almost touch the door surface. Making a latch with one handle that works for either either right or left hand doors is also no problem. Fishing reels are made so that the handle can be mounted for either right or left hand operation, so door handles would be a cinch. One way would be to make an elongated “knob” that pivots in the center and is long and slender with the ends bent down to prevent snagging things.
We use door knobs because we’ve always done it that way, and that’s such a powerful reason that reason is virtually powerless against it.
I’m sure my cats could open door handles - the Siamese already knows how to work the door knob, he just can’t get a grip on it. Thank goodness!
Oh, come on! You can’t get into these beauties? Even Aunt Clara on Bewitched used to collect doorknobs!
You can have our door knobs when they slip out of our cold dead hands!
(Wait a minute. I’m not sure that really works.)