I've always found it amusing that somehow custom silicon makes economic sense in the absolute cheapest products.
You look inside a child's toy? A musical greeting card? A remote control? A $5 multimeter? ASIC. Often in the form of a black epoxy blob 'chip on board'.
You look inside a $30,000 industrial robot arm? No no no, we couldn't possibly afford custom silicon, FPGAs are the only option.
First of all the epoxy blob may well contain a mostly off-the-shelf SOC, maybe lightly customized (mask programmed ROM, choice of peripherals). Not a full custom design.
Second, volume! If you're going to make a million of something, the NRE of a relatively low-tech chip isn't so bad.
Also, FPGAs can be reprogrammed in the field if necessary.
Volume dominates here for the same reasons a standard sized screw / bolt will be used anywhere possible. (If even needed at all, the analogy falls apart for seam welded plastics.)
The toys are also designed as make once and trash, since that's their sales model. The environmental costs of the resources aren't correctly factored in to the overall price. That super expensive robot arm is a tool that needs to work, it's economic value is in continued production. Modular components that can be replaced are more valued here to make warranty repairs and out of warranty field service possible. The customers literally demand and pay for that functionality.
The robot arm isn't running off a battery and most of them are large enough that board size isn't a constraint, so why add the complexity of custom silicon if it isn't needed? Using off-the-shelf FPGAs also makes repairs easier.
The context here was making 1000 chips. Custom. You amortize (decide whether it's worth it) based on the 1000 chips.
So yeah, if you are going to churn out a million greeting cards, you might do a very simple and relatively inexpensive custom design (say not very many standard cells plain logic plus ROM of the exact size you need, slow, on a conservative node), and get a million slightly smaller custom chips and come ahead.
If you are going to ship a thousand robot arms. You might need a high performance chip costly to design - and would only amortize that design cost over 1400 chips. So no, you may or may not be able to afford that design, that's not the issue. The issue is that it's not worth it. If it's an expensive military robot arm that launches missiles, you stuff 4-5 FPGAs in there. If it's a cheap robot arm, you stuff a Raspberry Pi in there. Either way, no custom chip for you and it's not a question of "couldn't possibly afford custom silicon".
That's a tall order - off the shelf is rarely very expensive for the functionality you get (that is, compared to design cost.)
And that's not necessary. If you could get a chip much more expensive but with specific advantages, you'd already have a business. See FPGAs.