In my experience, when chips are expensive (for non-supply reasons), it's usually for one of three reasons:

1. There's nothing else like it on the market, so the manufacturer can charge whatever price they want, and designers will still buy those chips (that last part is critical). (e.g. certain specialized chips from Analog Devices)

2. The manufacturer's costs are out of control. This is rare today, but was common in the '80s and '90s. Most of those companies went bust or were acquired, and now the semiconductor design industry is extremely focused on cost efficiency.

3. The manufacturer can't sell enough chips at a competitive price to pay back the NRE costs of the design + a reasonable margin, so they're forced to sell at a higher price. If they don't have other products, and are not able to diversify or sell the company, this is a death spiral.

For FTDI, (1) is clearly not the case -- they have lots of competitors, and the task that their chips perform (shoveling bytes around) is a basic one. FTDI's primary office is in Glasgow, Scotland, and they have satellite offices in China, Taiwan, Singapore, and the US. Their offices are tiny. (2) seems unlikely.

That only leaves option (3). The semiconductor business is famously reliant on volume, and this is especially true for low-cost, small-die-area designs. You need to sell a metric fuckton of chips if you're selling them for a few dollars each. And the only way to get that kind of volume is to secure design wins in high-volume consumer electronic products that sell by the metric fuckton.

Most of FTDI's volume appears to be in legacy products. Products that used to have a serial port, but that now need a USB port because computers don't have serial ports anymore. They make a few higher performance parts that seem to be designed specifically for FPGA vendors, because FPGAs often need a way to get as many Gbps as possible over a USB port, and FPGA vendors don't particularly care about an extra $20 chip, because their FPGA already costs $1000 and they don't want to muck-up their low-voltage process or waste pins and die area to support USB. Also the FPGA vendors picked FTDI ages ago, and don't want to rewrite their shitty, shitty software.

But you'll never see that FPGA USB-serdes chip designed into a laptop or a phone or a camera, because there are cheaper options available, and because the functionality can be had essentially for free when integrated onto the high performance SoC that requires it.

FTDI probably has enough volume on their legacy chips to cover their costs, but that's because the design is ancient and was paid off years ago, and because there are a lot of legacy industrial products that aren't going away anytime soon. The fact that they're still overpriced relative to competitors means they're not a product of choice for new designs, and are a particularly obvious candidate for cost-reductions. I don't know anyone who willingly designs in an FT2232 when a CP2104 will do the trick, especially after FTDI flushed their reputation away with that driver fiasco. So this part of their business is likely to shrink.

The FPGA vendors sell maybe a few thousand units of their $1000 - $10,000 FPGA boards. That's probably not enough volume to cover the costs of FTDI's higher performance chips, even at $20 a pop.

The sad thing is that (1) used to be true, back when USB was new, and there were a lot of buggy implementations. FTDI got it right, and they even had a reputation for a driver that "just worked." The answer to the question "How do I do USB?" used to be "Just shut up and buy an FTDI chip." An enviable position at the time, but as USB became more ubiquitous and better understood, their competitors caught up. Other vendors have good implementations and good drivers now. Good USB IP for chip designs is also readily available, so many microcontroller designs can do without FTDI now.

The FTDI driver fiasco was the worst thing they could have possibly done with the one thing they still had going for them -- they trashed the reputation of the quality of their driver, and now everyone looks at them with suspicion. Normally you would expect a semiconductor company with a limited, overpriced product line to be an acquisition target, but the fact that this hasn't happened despite the fact that they're a relatively small target suggests that the bigger players either looked at their books or did the math and realized that their market is shrinking and they have no growth prospects.

tl;dr

FTDI may not be doing as well as you think they are. Rather than doing well because their chips "command a high price" -- every indication suggests that they are resting on their laurels, they know their long-term prospects are grim, and are trying to squeeze out as much as they can before they go bust or are forced to sell themselves for scrap.