Federated learning (FL) has emerged as a transformative paradigm for edge intelligence, enabling collaborative model training while preserving data privacy across distributed personal devices. However, the inherent volatility of edge environments, characterized by dynamic resource availability and heterogeneous client capabilities, poses significant challenges for achieving high accuracy and fairness in client participation. This paper investigates the fundamental trade-off between model accuracy and fairness in highly volatile edge environments. This paper provides an extensive empirical evaluation of fairness-based client selection algorithms such as RBFF and RBCSF against random and greedy client selection regarding fairness, model performance, and time, in three benchmarking datasets (CIFAR10, FashionMNIST, and EMNIST). This work aims to shed light on the fairness-performance and fairness-speed trade-offs in a volatile edge environment and explore potential future research opportunities to address existing pitfalls in \textit{fair client selection} strategies in FL. Our results indicate that more equitable client selection algorithms, while providing a marginally better opportunity among clients, can result in slower global training in volatile environments\footnote{The code for our experiments can be found at https://github.com/obaidullahzaland/FairFL_FLTA.