Wars are meant to achieve political objectives, not to win battles, inflict casualty, take territory. It just so happens that achieving political objectives often involves winning battles and such.Taking Bahkmut at best is just a psychological victory. On the other hand, taking south means cutting off the Russian land bridge and isolating Russian military in South front which is a strategical victory.
If Ukraine decided to abandon the attack on south front and focus on the Bahkmut, then the counter offensive is already failed.
In this particular case, achieving a decisive military victory over Russia is IMO highly improbable. Propaganda victory is IMO what Ukraine needs to seek. This keeps Western support coming, which is critical as this is not an Ukraine vs Russia war at his point, this is a NATO vs Russia war. The moment NATO support wanes is the moment Ukraine loses.
To this end, I wonder if it's possible that Ukraine can yet refocus on Bakhmut. If they can retake it I'm sure you'll get endless snipes from Prigozhin as well about how he took Bakhmut and then the MOD lost it. That'll be enough headlines in the MSM to help sustain the war for quite a while longer.