I can, as a lay person interested in qm, try to explain some of David Deutsch words, hopefully successfully:
First of all, Copenhagen is taught by default at universities - they teach it as if it's the standard or most obvious interpretation - which means that most physicists who aren't interested in investigating the question of interpretation are possibly naturally predisposed to answer "Copenhagen" by default. If you don't ever bother to think about the question, you'll just say what you're teachers and your textbook say.
Secondly, the Copenhagen interpretation is also sometimes called "shut up and calculate" - shut up and calculate is not an interpretation, it's an anti interpretation. It's saying "we don't need to interpret what's happening, we just need to use the models to make useful predictions". That's fine as an opinion, but it's not an interpretation, it doesn't give us an idea of what's really going on with quantum experiments, which is exactly what quantum interpretations are supposed to do - they're supposed to tell us what's really going on. Not all Copenhagen interpretationsists will say that it's just shut up and calculate, some of them will say it's a real interpretation with real consequences for how the world works and why quantum mechanics gives good predictions.
David Deutsch is a physicist and he speaks to a lot of physicists, which means that he may have a deeper understanding of the views of his fellow physicists than can be accurately gathered in a poll. He may, in his experience talking to thousands of other physicists, have learned that one of the above two explanations - or both to some degree - explain why most physicists write down "Copenhagen" when asked for their preferred interpretation. Most of them may choose that because they simply prefer not to think about interpretations at all. It's also possible that he's just wrong, and you should take the poll results at face value.
I don't know if he's correct or not, I haven't spoken with thousands of physicists. Copenhagen seems like a particularly bad choice to me, because it conflicts with Relativity, but what do I know?