The reason the take-home assignment is unfair isn't because of a lack of objectivity. The unfairness is that it allows employers to make candidates spend proportionally more of the time, money, and effort required to generate signal from noise. Companies that are that aggressive at cost-cutting at your expense are also likely to have other strategies - say, giving the coding assignment to almost anyone and dropping the top 95% by salary requirement.

The short of it is that it's a candidate-unfriendly measure, and in my experience has been correlated with having other red flags.