It's important to remember that it's also YOU interviewing THEM. The coding interview is an opportunity to get to know the company culture in a very feet-on-the-ground fashion. How the interviewer behaves and how they expect you to do things reflects upon them as managers, mentors, and in general people you'll be working with for potentially a long time. - If they're forcing you to go against your natural flow, that'…
I agree with what you said in the rest of the comment, but I'd like to go one step further with the idea of "YOU interviewing THEM". Let's add some symmetry!
Let's make the interview double the usual time, and half of it I get to ask the other side to solve LC problems that I pick at random, or design systems I made up the day before, or behavioural questions about their past experiences. According to companies, that is the only way to assess if a person is good enough for the job, so I'd like to use the same method to find out if I want to work there.