The existence of certain types of moral standards (whether objective or subjective) doesn't necessarily correlate with the willingness of people to comply with said morals.
That being said, one can make an argument for the superiority of an objective (absolute) standard over the subjective (relative) standard because an objective standard applies equally to all people, and hence appeals of our sense of Justice and Equality (which is seemingly a good thing, pardon the pun, to have). Subjective moral standards give rise to hypocrisy ('Why it is okay for me, but not them?'), which in turns leads to inconsistency and finally rejection of said moral standards. For example, there are certain moral principles which are perceived as absolute (unjustified killing of humans is wrong etc) and since they apply universally, it would make people more willing to follow them out of the need for consistency.
PS. I am someone who believes in a absolute/objective moral standard, and I am willing to bet a lot of people are. I've found that a lot of people who say they are moral relativists or nihilists do not understand the implications that such a belief system holds. They prob just want to be edgy (nihilism is a pretty young philosophy).