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There are no benefits in doing something that cannot be done. The standard normal distribution is not transformed to the standard distribution because the latter does not exist.
The standard deviation in a standard normal distribution is 1.
The standard deviation in a standard normal distribution is 1.
The standard normal distribution is a special case normal distribution, which has a mean of zero and a standard deviation of one.
The normal distribution is very difficult to work with: the probability density function is not simple [I suspect that only a few mathematics graduates from university would be able to integrate it!]. The standard normal has been tabulated in considerable detail and so, if the normal is transformed to the standard normal, most of the analyses, hypothesis testing, confidence intervals and so on can be found by looking up tables.