At the heart of many nucleoside triphosphatases is a conserved phosphate-binding sequence motif. A current model of early enzyme evolution proposes that this 6-8 residue motif could have sparked the emergence of the very first nucleoside triphosphatases - a striking example of evolutionary continuity from simple beginnings, if true. To test this provocative model, seven disembodied Walker A-derived peptides were extensively computationally characterized. Although dynamic flickers of nest-like conformations were observed, significant structural similarity between the situated peptide and its disembodied counterpart was not detected. Simulations suggest that phosphate binding is non-specific, with a preference for GTP over orthophosphate. Control peptides with the same amino acid composition but different sequences and situated conformations behaved similarly to the Walker A peptides, revealing no indication that the Walker A sequence is privileged as a disembodied peptide. We conclude that the evolutionary history of the P-Loop NTPase family is unlikely to have started with a disembodied Walker A peptide in an aqueous environment. The limits of evolutionary continuity for this protein family must be reconsidered. Finally, we argue that motifs such as the Walker A motif may represent incomplete or fragmentary molecular fossils - the true nature of which have been eroded by time.