Suppose that we have the following model
$Y = b_{0}+b_{1}*Season +b_{2}*Income$
In order for $b_{0}$ to refer to the expected value of $Y$, we should center the variables Season and Income. However, what would be the meaning of centering such a variable ?? How we are supposed to interpret $Season-\overline{Season}$??
The intercept, included in the regression equation implies that the value of Y when the predictors are zero. Since you are adding the season as one of the predictor variables, it implies that the there will be no occurrence or case where all the predictor variables would be zero. Income can be zero sometimes but season can't be. In such situation, the interpretation of the intercept will not make much sense.
In order to make proper interpretation of the intercept, it is advisable to center the predictor variable which is not having a zero in real. Centering the variable means that the variable will be deducted from it's own mean as mentioned by you, so that we could have the data set with a probable zero and the zero value of the predictor would also make sense.
In this case, we would have a concrete meaning for the intercept included in the model.
