The Battle of Bakhmut was part of summer offensive operations for the Russians aimed at a large encirclement of Ukrainian forces. Ukraine’s retaking of Izyum meant this strategic goal was null, but Russia continued assaults on Bakhmut anyway. They did this, not to support a strategic goal of limiting Ukrainian offensive power, but to promote the propaganda goal of giving Russia a victory after a very bad summer of defeats. Ukraine had already fought its offensive, and had liberated large parts of Kherson and Kharkiv oblasts.
Regarding units involved and casualties - prior to the Wagner / convict forces becoming the main body in Bakhmut, the Russian Army did suffer serious losses of conventional forces - i.e. the 144th Guards Motor Rifle Division was destroyed by September and several Russian VDV units suffered heavy attritional losses throughout the campaign.
Once the battle did get into winter, and Wagner started largely replacing Russian Army units, fighting outside of the city resembled that of Passchendale in 1917 with a cold, muddy, deforested landscape being crisscrossed by trenches. The fighting was horribly slow and brutal, highlighting why you wouldn’t see major offensive operations on any other front during this time frame - it would have led to the same result. Fighting inside of the city would obviously be fought in different terrain, but again, urban operations heavily favor the defender, even with a tiny fraction of the manpower of the offensive force, and history tells us that the attacker would suffer greatly, even without the problems caused by mud. Wagner’s convict forces were largely exhausted by the end of January, meaning Wagner had to once again commit its good units into the fight from February until the end of major operations in May.