What will happen if you do not convert all characters to a single case (either lower or upper) during the pre-processing step of an NLP algorithm?

When all words are not converted  to a single case, the vocabulary size will increase drastically as words like Up/up or Fast/fast or This/this will be treated differently which isn’t a correct behaviour for the NLP task. Sparsity is higher when building the language model since the cat is  treated differently from The cat. Suppose…