Behavioral Timescale Synaptic Plasticity (BTSP) is a type of synaptic plasticity in which large, Ca2+ plateau potentials in hippocampal pyramidal cells drive the formation of hippocampal fields such as place fields. BTSP differentiates itself from typical forms of plasticity by a) learning pre-post correlations on the timescales of seconds and b) learning in a one-to-few-shot manner. Though BTSP has been posited to be the primary driver of field formation in hippocampus, theoretical models that describe the population-level computations of hippocampus (such as the formation of "cognitive" or "predictive" maps) do not use BTSP. Instead, these models use supervised or predictive learning rules that require a) precise spatiotemporal credit assignment, and b) thousands of trials of training. To investigate the feasibility of BTSP as a learning rule in both CA1-like feed-forward and CA3-like recurrent networks, we introduce a generalized BTSP rule (gBTSP) in neural networks that are then task-optimised. While we demonstrate that gBTSP can successfully learn in both feed-forward and recurrent networks, important experimental features of BTSP such as few-shot learning are only possible in shallow feed-forward tasks. We show analytically that the one-to-few shot learning observed via BTSP is incompatible with generic recurrent networks, being critically restricted by exploding/vanishing task-error gradients. However, we demonstrate that pre-training recurrent networks may enable few-shot learning in selective contexts. Our work proposes a generalized theoretical rule for BTSP, and shows that for recurrent networks (like CA3), the few-shot nature of BTSP is a fundamental impediment to effective credit assignment. This work lays the foundation for further investigation into how we can reconcile experimentally observed constraints imposed by BTSP with the recent success of task-optimised hippocampal models.