If we have the linear model $Y_i-\bar{Y} =b(X_i - \bar{X}) + \varepsilon_i,\ i=1,..., n$ , then we can find easily an unbiased estimator $b^*$ for $b$ with the least squares method. If $c=(Y_n - \bar{Y})/(X_n - \bar{X})$ is another unbiased estimator, then which one is better to choose? I believe that the least squares estimator is better for the linear model because it minimizes the distance of the observations $Y_i - \bar{Y}$ from regression line, which means that the SSE is smaller. Therefore the SSR is closer to SST, and that means that $R^2$ is closer to 1, which I know is not always what we want, however I believe that it could be one reason that $b^*$ is more preferable than $c$.
Is my thought correct, and if it is, is there any other reason why we choose $b^*$ than $c$, and if it is false, can someone explain why?