Because the bootstrapped statistic is one further abstraction away from your population parameter. You have your population parameter, your sample statistic, and only on the third layer you have the bootstrap. The bootstrapped mean value is not a better estimator for your population parameter. It's merely an estimate of an estimate.
As $n \rightarrow \infty$ the bootstrap distribution containing all possible bootstrapped combinations centers around the sample statistic much like the sample statistic centers around the population parameter under the same conditions. This paper here sums these things up quite nicely and it's one of the easiest I could find. For more detailed proofs follow the papers they're referencing. Noteworthy examples are Efron (1979) and Singh (1981)
The bootstrapped distribution of $\theta_B - \hat\theta$ follows the distribution of $\hat \theta - \theta$ which makes it useful in the estimation of the standard error of a sample estimate, in the construction of confidence intervals, and in the estimation of a parameter's bias. It does not make it a better estimator for the population's parameter. It merely offers a sometimes better alternative to the usual parametric distribution for the statistic's distribution.