Some level of privacy, yes. Solely in WhatsApp-signal chats. And users can be notified of that, like they were with SMS.
But you know what the alternative is? Nobody using signal. And that's objectively worse.
Cross-compatibility with WhatsApp would mean way more people on signal, and way more people willing to try, meaning more signal-signal chats. Meta would scrape metadata like when two accounts send messages and the like, but the contents of the chats would of course still be E2EE.
Signal-SMS is FAR less private, but they were fine with that for years, and people are still angry about it being removed.
Cross-compatibility removes the biggest hurdle for Signal - the chicken and egg problem of nobody using signal because they can't talk to anyone. It would act as a Trojan horse for pushing signal-signal communication.