RL Sutton book, initial estimate of q*(a) for 10 arm testbed
The description you quote explains how the true values will be set in the test when setting up a test run. This is necessary to fully state how the test works.

Initialisation of your estimates is a different issue. If you know something about the distributions of the true action values, then it would make sense to use that. For instance you could set all action values to the mean expected true value. Which is $0$. However, you may also use $0$ if you have no idea about true values, as it is a simple arbitrary value.

Setting the estimates to something using the same distribution is not unreasonable, as it that itself is an unbiased estimate of the same mean. However, it does not really serve you well here, because it adds variance to the initial estimates (as well as possibilty of them being closer to true values, they are equally likely to be worse) and on average slowing down some agent types slightly.