Still, with the 2 bridges out of commission, Russian supply lines are threatened and it becomes a case of defense of logistics. If the Russians commit more forces to defend it, this makes supplying them more problematic and they are at more risk of losing more troops. If they insert too few troops they may not be able to hold the region. If this occurs the Russians plans of encircling the Ukrainian forces to the Northeast of this map (Eastern Ukraine) will likely not materialize. To this point the Ukrainians have been unable to obtain the heavy weaponry needed to take Kherson. The Russians have more than doubled their forces in the region and made gains pushing back the Ukrainian forces during good weather. It appears Ukraine may instead be waiting for the onset of winter when the Russians lose much of their tactical heavy equipment advantage, rather than wait for assistance from the Western nations which has been slow to materialize as promised.
Ukraine very much needs this victory to help secure continued assistance and a supply of weapons from the NATO nations. If Ukraine can seize Kherson they will be able to transfer many of their forces in the South to further bolster their Eastern defenses or even make inroads into the Crimea itself.