The reason is that these edge cases often expose where the current models can break down.
If the current accepted theory is predicting negative mass or infinite mass, it doesn't really mean that a physicist deeply believes we are going to be finding particles with negative mass. It's more likely we'll find a better theory.
In some rare cases, these mathematical oddities do turn out to be real. We found equations producing negative energy as solutions long before we discovered antimatter.
If the current accepted theory is predicting negative mass or infinite mass, it doesn't really mean that a physicist deeply believes we are going to be finding particles with negative mass. It's more likely we'll find a better theory.
In some rare cases, these mathematical oddities do turn out to be real. We found equations producing negative energy as solutions long before we discovered antimatter.