The answer is very straight-forward: TF-IDF can achieve better results than simple term frequencies when combined with some supervised methods.
The canonical example is using cosine similarity as a measurement of similarity between documents. Taking the cosine of the angle between the TF-IDF vector representation of documents can successfully retrieve relevant similar documents with higher accuracy than TF alone.
This is because IDF reduces the weight given to common words, and highlights the uncommon words in a document. Most news articles aren't about ostriches, so a news article containing "ostrich" is unusual, and we'd like to know that when trying to find documents that are similar.
But in the case of text categorization using standard supervised ML techniques, why bother downweighting by the frequency of documents in the corpus? Will not the learner itself decide the importance to assign to each word/combination of words?
This illustrates a key point in machine learning: better features tend to beat a cleverer algorithm. An ML tool is just trying to learn a function to map input(s) $x$ to output(s) $y$. If our representation of $x$ is so good that they are already basically $y$ (or, in an ideal case, literally are $y$), then we've made the task much easier on ourselves, and our poor, overworked computers! I think this is an under-appreciated component of the field -- people spend lots of time studying and considering the algorithms because they are domain-independent, but knowing more about your data and the problem you're trying to solve can suggest paths to improved data collection or data representation which make the task so much easier -- and so easy that a model of ornate sophistication is unnecessary.
A number of resources can be found here, which I reproduce for convenience.
K. Sparck Jones. "A statistical interpretation of term specificity
and its application in retrieval". Journal of Documentation, 28 (1).
G. Salton and Edward Fox and Wu Harry Wu. "Extended Boolean
information retrieval". Communications of the ACM, 26 (11). 1983.
G. Salton and M. J. McGill. "Introduction to modern information
G. Salton and C. Buckley. "Term-weighting approaches in automatic
text retrieval". Information Processing & Management, 24 (5). 1988.
H. Wu and R. Luk and K. Wong and K. Kwok. "Interpreting TF-IDF term
weights as making relevance decisions". ACM Transactions on
Information Systems, 26 (3). 2008.