For moral relativism not to exist, then there would have to be just one correct moral answer to every moral problem.
No. For moral relativism not to exist there would have to exist a body of uniquely “moral” acts or behaviours with one, or possibly even several possible correct answers. Those “moral” conditions would not need to apply universally to every choice or act, only to uniquely “moral” choices or acts.
It could be true that some problems in the human condition are not moral problems at all - they may be practical problems or aesthetic problems, etc. and these would be allowed a divergence of possible solutions.
For relativism to be true, i.e., that no true moral perspective exists, that requires that no real moral problems exist AT ALL. That there are NO uniquely “moral” issues with no uniquely “moral” solutions to which all moral agents are obligated.
It may actually be true that some moral problems allow several solutions and moral agents are obligated to choose one of several possible answers. That is still NOT relativism.
When I ponder whether to wear brown socks instead of blue, I am not engaging in a moral dilemma. It doesn’t “really” matter which colour I wear so the issue is not important from a moral perspective.
For moral relativism to be true it would reduce all dilemmas to the level of choosing socks. For moral relativism to be true, It wouldn’t “really” matter which way you chose even in what are ostensibly “moral” issues because relativism insists that morality is simply a matter of personal preference, like choosing socks.
For moral relativism to be true “absolutely” there would be nothing like “moral” repercussions. There would be no morally “good” or “bad” acts or decisions, merely what you prefer and what I prefer. There would be no ground, if morality were, indeed, preferential or relative, for saying one preference is “right” and another “wrong.”
Relativism is not merely incoherent, it is insane. Only someone out of touch with reality would claim murder and rape are merely distasteful and carry nothing like objective moral condemnation. Clearly rape and murder are objectively morally wrong and merely because there exist some, or even many, immoral or amoral individuals, who deny that these acts are “wrong” in a properly moral sense, does not make their position a valid “moral” one.
Moral agents can become immoral or amoral, but that “fact” does not make their abdication of morality legitimate no matter how much they insist that it is. Moral agents are bound by moral constraints. Moral agency cannot be unilaterally cast off because it is embedded in our very nature as rational moral beings. Our decisions and acts matter morally and we are keenly aware of that fact. Denial does not make morality evaporate.