You appear to be operating under some misunderstanding - your question seems to rely on a false premise.
If you're trying to give a point estimate of the mean of the distribution of sample means, that would indeed (often) be the sample mean.
The standard error of the mean is used to give some idea of the associated uncertainty in the location of the mean of that distribution. The standard error of the mean is the standard deviation of the distribution of sample means. It tells you something about how far away from the thing you're trying to estimate your sample mean will typically be.
e.g. if you wanted to give a confidence interval for that population mean of the distribution of sample means, it would typically be based on that sample mean $\pm$ a margin of error (interval halfwidth) that is a multiple of that standard error.