Bag-of-words model : Boolean vs. TF-IDF
Your reasoning is correct: for most tasks related to information retrieval and/or document classification based on the semantics of the documents, it's recommended to take into account the importance of the terms (both inside the document and across all documents, hence TF and IDF).

However TF-IDF is not necessarily always the best choice:


There are some classification tasks which are not based on the semantics of the document. For example if the goal is to classify documents by writing style (e.g. find documents by the same author) then the topic doesn't matter and therefore IDF is not relevant. 
In the case of a very small dataset and/or very short documents, using TF-IDF scores can lead to overfitting. In such cases using boolean values might perform better because it makes the job of the model easier.