To me that's kind of gross even for a meat eater, especially since we've been trained to make sure ground meat is fully cooked to 165F to assure there's no surviving e coli in all the surfaces in the mixed together bits of ground meat. If I got a burger that bled red juices, I'd be very put off by that - if it really has the same texture and taste as ground beef, how could I be sure they didn't accidentally give me real ground beef that didn't get cooked thoroughly?

Steaks and roasts are a different matter - those can have bloody looking juices inside because they only have surface meat on the outside of the piece of meat.