The ACTUAL manufacturing costs are probably WELL below the $0.20 that you mention, but that's not the point.
(If it was, I'd expect to be purchasing an I7-Haswell Intel CPU for only a couple of dollars!)
The 'production cost' of almost ANY given chip is almost incidental once you've built yourself a suitable fab and also spent all the time and effort in the R&D of the chip design.
Looking on Digikey, the current RETAIL price of a (genuine? who knows these days) FT232RL / SSOP28 in one-off quantities is NZ$6.34 which lowers to NZ$4.29958 in 500 quantity.
That's somewhat MORE than (for example) a Silabs CP2102 /QFN-28 at only $NZ3.88 each
The R&D costs between the two chips would, I assume, be in the same ballpark and I'd expect the production costs to be equally in the same ballpark. Therefore, I would bet it's fairly safe to assume that FTDI (and every other 'middleman' in the supply chain) is making about 100% more profit on a FT232RL than on a CP2102.
It's surmised that at least SOME of the clones are simply a repurposed microcontroller. (One that already had USB and a UART seems obvious). I would think I could knock up the firmware to 'emulate' a FTDI in a day or two (given the FTDI datasheet). (i.e. The R&D costs would be insignificant - near ZERO). The cheapest Atmel with USB and UART I could find on digikey is NZ$4.30 each. For a suitable PIC, it'd be NZ$2.11 each.
I'm pretty sure I could 'approach' either of them with a request to supply a million 'pre-programmed' chips in a non-standard case. (Or just buy a million 'bare die' and have them encapsulated in shenzen etc.)
I'm sure as hell not going to though... That's why they invented Chinese. Much like the japs of yesteryear, they're incapable of inventing anything much of significance (well, not since fireworks anyway). All they can do is COPY stuff very cheaply in the myriad Chinese sweatshops. Heck, just looking at them they're already almost 'copies' of each other??? <Evil Grins @ the 'stereotype'>
IMNShO, companies in the 21st century should NOT be allowed to 'rest on their laurels'. I considers patents and copyrights EVIL devices designed to holdback progress and innovation. I believe it's far better to be out 'inventing a new / novel mouse trap' than to waste time protecting last weeks mouse trap.
The only downside is that the exponential rate of advancement is becoming progressively more difficult for Joe Average to keep up with. (By the time Windows 11 is released, we'll be required to 'reboot it' every 5 seconds. Back in the Win 98 days we were allowed to wait 5 mins before it needed a reboot).