All assessment is to a certain degree subjective, and that's good so. It is plain wrong to prefer so-called objective tests as the only viable way of assessing knowledge, skills and performance. Just because so-called objective assessment may be easier to "control", "manage" or "apply" than so-called subjective assessment doesn't make them intrinsically better. Moreover, nowadays there is a resurgence and broad acceptance of authentic assessment as being more realistic than either subjective or objective. Authentic assessment however is almost always partly subjective, partly objective, because there are no good general ways of testing it on the basis of good old testing theory / methodology. Finally, subjective testing IS the standard in many branches and fields of education: arts and music, sports and dress, etc.
I understand everyone learns different. I also understand that some people handle objective assessments, such as tests, better than others. However, controlling a subjective assessment would be extremely difficult. When does subjective become too subjective. And the decision on this is subjective in itself. So while it may seem like a fair idea, it would be difficult to implement simply because there would be too many biases.
For some people subjective assessments are better. For other people objective assessments are better. Neither one is better than the other. Every person reacts differently to each assessment and what might be better for one person, is worse for another. Subjective and objective assessments are no better or worse than each other.