What if a Service pops up. They take your Bitcoin and send you a Monero Private Key. It looks like an Exchange but it is not. They never call themselves a 'Mixer' nor do they seem like one at first glance. The functionality is exactly like Chip Mixer but the Currency you receive in the end is not Bitcoin but Monero instead.
Why give users a private key, instead of sending Monero to an address? It sounds like an exchange with increased risk.
My guess is he thinks his method is not a mixer.
Your idea would be a mixer.
ie he thinks he has a workaround.