Every day, our inboxes are flooded with unsolicited emails, ranging between annoying spam to more subtle phishing scams. Unfortunately, despite abundant prior efforts proposing solutions achieving near-perfect accuracy, the reality is that countering malicious emails still remains an unsolved dilemma. This "open problem" paper carries out a critical assessment of scientific works in the context of phishing email detection. First, we focus on the benchmark datasets that have been used to assess the methods proposed in research. We find that most prior work relied on datasets containing emails that -- we argue -- are not representative of current trends, and mostly encompass the English language. Based on this finding, we then re-implement and re-assess a variety of detection methods reliant on machine learning (ML), including large-language models (LLM), and release all of our codebase -- an (unfortunately) uncommon practice in related research. We show that most such methods achieve near-perfect performance when trained and tested on the same dataset -- a result which intrinsically hinders development (how can future research outperform methods that are already near perfect?). To foster the creation of "more challenging benchmarks" that reflect current phishing trends, we propose E-PhishGEN, an LLM-based (and privacy-savvy) framework to generate novel phishing-email datasets. We use our E-PhishGEN to create E-PhishLLM, a novel phishing-email detection dataset containing 16616 emails in three languages. We use E-PhishLLM to test the detectors we considered, showing a much lower performance than that achieved on existing benchmarks -- indicating a larger room for improvement. We also validate the quality of E-PhishLLM with a user study (n=30). To sum up, we show that phishing email detection is still an open problem -- and provide the means to tackle such a problem by future research.