Etsy also ships physical things, the only difference is that they subcontract to a delivery company, who obviously doesn't pay taxes over Etsy's profits.

But actually, it's not different, because Amazon also subcontracts, the only difference is that the subcontracted delivery company is named... Amazon. So what they're doing is the same as any companies that ships products to the UK, except that they happen to own both companies and they have similar names.

I fail to see the reason why should Amazon UK pay for the profits earned by Amazon Luxembourg, when DHL or whoever don't pay for Etsy's profits that come from the UK.