Is converting a numerical target to binary helpful?
When you convert a variable from numerical to binary, what happens is that you lose information about the magnitude of the variable and summarise it into a &gt;=X variable.

It has advantages and disadvantages depending on the use you will give to your model:

If your model has to determine the exact amount of "how high" is your pollution, then is not a good idea to convert it because you are loosing crucial information, but if the city major declares a curfew if the pollution is bigger than x, then a binary output is not only good idea but necessary for the decision you are achieving with it.

When you convert the variable to binary, the hypothetical model you are achieving has different kind of information that the model with numerical variables:


You will not be comparing exact values (measuring RMSE), you will be measuring membership to a set (measuring AUC).
If your client wants to measure wheter you trespassed or not a threshold, you should explain to him what is achievable with that model and ask him it that meets the requirements of his job.