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Before the Quidditch World Cup, Mr. Crouch Sr. says:

“Oh and I’ve been wanting a word with you too, Arthur,” said Mr. Crouch, his sharp eyes falling upon Mr. Weasley. “Ali Bashir’s on the warpath. He wants a word with you about your embargo on flying carpets.”

Mr. Weasley heaved a deep sigh.

“I sent him an owl about that just last week. If I’ve told him once I’ve told him a hundred times: Carpets are defined as a Muggle Ar­tifact by the Registry of Proscribed Charmable Objects, but will he listen?”

...

“Ali thinks there’s a niche in the market for a family vehicle,” said Mr. Crouch. “I remember my grandfather had an Axminster that could seat twelve — but that was before carpets were banned, of course.”

From this we can see that it was Arthur Weasley who banned carpets, because Crouch calls it "your embargo". That means this ban can not be older than Arthur, and in fact should be quite recent, as Arthur was not born into his position at the ministry. As Mr. Crouch says, he remembers that his grandfather had a (flying) carpet, he has seen it and probably was allowed to fly on it when he was younger.

On the other hand, flying brooms are obviously not banned, otherwise there would be no flying lessons and no Quidditch.

The reason Arthur gives is that they are Muggle Ar­tifacts. But so are brooms. While the original books don't mention anything about the origin of flying brooms, Quidditch Through the Ages says that brooms were chosen because they were Muggle Ar­tifacts.

If (wizards and witches) were to keep a means of flight in their houses, it would necessarily be something discreet, something easy to hide. The broomstick was ideal for this purpose; it required no explanation, no excuse if found by Muggles.

The same is true for a carpet, it requires no explanation, no excuse if found by Muggles.

So there is no factual reason to ban carpets but allow brooms.

One could argue cultural bias, but the fact that the ban is recent and carpets were used in England before the ban seems to invalidate that reasoning.

So why did Arthur ban carpets while he has no problem with brooms? He even created a loophole for flying cars, and nobody would deny that a car is a Muggle Ar­tifact.

Later we hear that

Ali Bashir was caught smuggling a consignment of flying carpets into the coun­try

If he is willing to take the risk, that means that there has to be some demand for carpets. They are not as popular as broom, but there is some demand, and they are certainly more convenient to use. What is the benefit that justifies to prohibit something a part of the population wants? Why would a charmed carpet be more dangerous than a charmed broom to Muggles?

It's probably down to culture.

Note Ludo Bagman's immediate scepticism to the idea that the carpet could supplant the broom.

“Well, they’ll never replace brooms in Britain, will they?” said Bagman.
_{(Goblet of Fire, Chapter 7, Bagman and Crouch).}

Flying carpets aren't banned everywhere. They are legal in Asia. The only place that we know where they are definitively banned is Britain.

Why should the humble broom have become the one object legally allowed as a means of wizarding transport? Why did we in the West not adopt the carpet so beloved of our Eastern brethren?
_{(Quidditch Through the Ages, Chapter 1, The Evolution of the Flying Broomstick).}

This quote also demonstrates that Britain has banned not only carpets but all forms of object-based transport other than brooms. Brooms are therefore the only object which one is "legally allowed" to use to travel with.

This suggests a strong cultural preference for brooms. In Britain the broom quickly took off (excuse the pun) in popularity. In Asia it was less popular and flying carpets were preferred (and therefore remained legal). Put it down to what wizards would put up with. Ban carpets and everyone apart from Ali Bashir has no problems. Ban the broom and there'd be uproar. Just look at the reaction when Dumbledore suggested suspending school Quidditch for a single year.

“It is also my painful duty to inform you that the Inter-House Quidditch Cup will not take place this year.”

“What?” Harry gasped. He looked around at Fred and George, his fellow members of the Quidditch team. They were mouthing soundlessly at Dumbledore, apparently too appalled to speak.
_{(Goblet of Fire, Chapter 12, The Triwizard Tournament).}

The way in which laws are written seems pretty haphazard and the democratic accountability fairly limited in the wizarding world. Nevertheless, Fudge was hounded from office so there clearly is some element of needing to keep the people happy. People in Britain loved brooms so they were the only form of object-based transport the Ministry didn't ban.

Why brooms were so much more popular than carpets from the early days isn't clear. However, there were qualities other than just being a Muggle object which was easy to hide. The advantage of the broom is hinted at just after the section of Quidditch Through the Ages quoted in the question.

If they were to keep a means of flight in their houses, it would necessarily be something discreet, something easy to hide. The broomstick was ideal for this purpose; it required no explanation, no excuse if found by Muggles, it was easily portable and inexpensive.
_{(Quidditch Through the Ages, Chapter 1, The Evolution of the Flying Broomstick).}

Flying carpets may well be just as good as flying brooms in other respects but it's not difficult to see why they would be seen as bulkier and more expensive to produce than brooms. Parking your carpet indoors is cumbersome. Parking a broom certainly isn't. Everyone has a broom. Perhaps not every wizard had a carpet to charm.

As for the legislation, this is the only time that we hear about the Registry of Proscribed Charmable Objects in canon. The timing and the nature of the ban aren't revealed anywhere but you're likely overstating Arthur Weasley's involvement. Crouch most likely described the embargo as "your embargo" because the enforcement of this particular law is Mr Weasley's job. The embargo is just the enforcement of the law, and the law seems to be longstanding (given how ludicrous the idea of people giving up brooms is). So this was almost certainly not Mr Weasley's ban.

I think you are reading too much into Crouch's use of your embargo.

Arthur says he didn't allow Ali Bashir to import flying carpets because they are on the "Registry of Proscribed Charmable Objects". The "embargo" may be Arthur's rejection of this particular import request.

Flying carpets could have been added to the "Registry of Proscribed Charmable Objects" any time after Crouch's grandfather acquired the flying Axminster.

We should probably not rule out cultural bias just because flying carpets were once allowed. These things can come and go based on random influences.