I’m not following your reasoning at all.
“It is not a matter of Japanese, but of English”
It actually is a matter of Japanese, as the translation is attempting to produce the closest meaning possible to what it is in JAPANESE. As you pointed out in your original post, no one says “three one thousand,” so 千, which is included in all forms of thousands 三千 included would be “three thousand.” Yes, 千円 is appropriate because that is the meaning of 千円, not 千. If I say “a hundred dollars,” you would understand that as “one hundred dollars,” correct? And yet, there is no confusion if I say “two hundred dollars” nor do you expect me to say “two one hundred” or “two a hundred” dollars.
You are justifying a specific translation for an umbrella term, which is quite backward logically. And why not complain about 百, which, from what I see, only allows “Hundred” as a kanji. Unlike 千, where 一千 is actually very common (I’ve had employees at my local supermarket say 一千円).
I think the basic flaw of your argument is the following:
“The problem has nothing to do with Japanese but with English which says
’one hundred’ and ‘one thousand’ where everybody else will use these
powers of ten without ‘one’ to express that there is only one.”
This is not entirely true, as it is completely fine and common to say “a hundred” or “a thousand.” Seeing as the articles “a,” “an,” and “the” do not translate to Japanese, that would be the exact translation. When dealing with multiples, we also say “thousands,” not “one thousands,” further denying this claim. There is actually no problem on the side of English syntax, rather your understanding of it.
As further proof, pop “If I Had” into your search bar and enjoy as “a million dollars” appears, not “one million dollars.” I hope this helps!