Linux SoC based designs are fairly complex in terms of engineering cost - if you're only building 10k of something, you might in fact be better off using something like the RPi Zero or Compute Module (or another system-on-module, like Variscite or etc.) rather than trying to integrate the Broadcom part yourself. Not to mention that RPi is getting much better prices on things like the SoC and the HDI PCB than a startup producing 10k of something is likely to get, so it may even be a wash on unit cost. And the supply risk is likely manageable; 10k is a high enough volume that it would be foolish to rely on distributor stock/spot prices for components, so you're already worrying about leadtimes; I don't see why a wholesale contract with RPi would be that much riskier. (Yes, it's true that the leadtime would increase a bit since RPi needs to purchase components themselves and convert them into modules.)
Now if your product is Arduino based (or another microcontroller platform) the barriers to doing a fully custom design are a lot lower, the markups on the Arduino board are a lot higher, and so the cutoff volume for where it makes sense to do a custom design is going to be much lower than 10k.
Now if your product is Arduino based (or another microcontroller platform) the barriers to doing a fully custom design are a lot lower, the markups on the Arduino board are a lot higher, and so the cutoff volume for where it makes sense to do a custom design is going to be much lower than 10k.