What exactly is stopping people from designing an open-source printer? Even if it is patents, surely many of them should have expired by now?

It's the size of the market. The startup cost of making a competitively cheap printer is much larger than the expected revenue. Would you pay $2000 for a whitebox printer? Would anyone? It'd be a cool passion project, but making a legitimate business out of it would be hard.

One big question I have: "is it legal to sell a printer that requires the use of someone else's toner?". If so, then the concern about sourcing toner after the whitebox company fails can be addressed in the design stage.

What I really want to know is why there is no BYOPK whitebox TPM product. That should be easy to make and could dominate the market.

Toner or ink shouldn't be much of a problem IMO — you can buy off-brand ink and toner for DIY cartridge refills for existing proprietary printers.