The use of large language models (LLMs) for relevance assessment in information retrieval has gained significant attention, with recent studies suggesting that LLM-based judgments provide comparable evaluations to human judgments. Notably, based on TREC 2024 data, Upadhyay et al make a bold claim that LLM-based relevance assessments, such as those generated by the Umbrela system, can fully replace traditional human relevance assessments in TREC-style evaluations. This paper critically examines this claim, highlighting practical and theoretical limitations that undermine the validity of this conclusion. First, we question whether the evidence provided by Upadhyay et al. genuinely supports their claim, particularly when the test collection is intended to serve as a benchmark for future research innovations.Second, we submit a system deliberately crafted to exploit automatic evaluation metrics, demonstrating that it can achieve artificially inflated scores without truly improving retrieval quality. Third, we simulate the consequences of circularity by analyzing Kendall's tau correlations under the hypothetical scenario in which all systems adopt Umbrela as a final-stage re-ranker, illustrating how reliance on LLM-based assessments can distort system rankings. Theoretical challenges - including the inherent narcissism of LLMs, the risk of overfitting to LLM-based metrics, and the potential degradation of future LLM performance - that must be addressed before LLM-based relevance assessments can be considered a viable replacement for human judgments.