Is it wrong to transform the target variable and test the model without dropping the column that was transformed? What's the disadvantage about it?
The problem is that, by definition, your target variable is not available at inference time, and that is why you want to predict it. If your target variable was available at inference time, then there is no point in predicting it.
Therefore, if you use the target variable (or a transformation of it) as input to your model, what data are you going to feed to that variable at inference time?