If one wanted to become a heavenly consort, the conditions were very harsh. Cultivation and strength were secondary. The key was to have the fate. For example, Liu Xueqing did not have that fate, so she could only become a heavenly concubine, and now she was an immortal consort.
The status of the heavenly court was somewhat similar to the status of The Fated Sky dynasty. Although it was illusory, it actually existed. And although the snow goddess was better than Liu Xueqing, she could not be forced to reach the status of heavenly consort.
If she forced herself to become a heavenly consort, the snow goddess's fate would be very miserable. She would either become a demon and be hated by all the heavenly concubines or suffer the backlash of the heavenly court's fate energy, causing her state of mind to be unbalanced and eventually walk on the wrong path.