For people who might be looking for an actual answer to the actual question: the application that prompted this question is now in production allowing only characters from the BMP (actually a limited subset).
Multiple international customers using Korean language in production - Japanese going live soon. Chinese is in planning (I have my doubts that the BMP will be sufficient for that, but we'll see I guess).
It's fine - no reported issues related to unsupported characters.
But that's just anecdotal evidence, really. Just because my customers were fine with it - that doesn't mean yours will be. For context, customers of the app are international companies, hundreds of employees using the application to process hundreds of thousands of their customers.