Most american, frum people in Yerushalayim won’t eat BBY.
The way someone once explained it to me is that R’ Ovadia created a hechsher for sephardim with the same idea in mind as the rabbanut. Ashkenazim have psakim that sephardim won’t rely on lihalach (ie. hashlachas kisem) and wanted an alternative. He knew everyone would listen to him, and made a hechsher that relies on lots of kulas so all the sephardim would at least eat that and not treif/plain rabbanut (which uses kulas that are totally unacceptable lihalacha for sphardim, as opposed to extremely bidi’eved for ashkenazim.) The bare standard for their chickens is actually very good, so it’s a shtikl funny: you end up with a hechsher that was created as a bidi’eved with very good chickens, and people think that reflects on the general hechsher, which it absolutely does not.