Lifetimes of the first excited 2^{+} and 4^{+} states in the extremely neutron-deficient nuclide ^{172}Pt have been measured for the first time using the recoil-distance Doppler shift and recoil-decay tagging techniques. An unusually low value of the ratio B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+})=0.55(19) was found, similar to a handful of other such anomalous cases observed in the entire Segré chart. The observation adds to a cluster of a few extremely neutron-deficient nuclides of the heavy transition metals with neutron numbers N≈90-94 featuring the effect. No theoretical model calculations reported to date have been able to explain the anomalously low B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+}) ratios observed in these cases. Such low values cannot, e.g., be explained within the framework of the geometrical collective model or by algebraic approaches within the interacting boson model framework. It is proposed that the group of B(E2:4_{1}^{+}→2_{1}^{+})/B(E2:2_{1}^{+}→0_{gs}^{+}) ratios in the extremely neutron-deficient even-even W, Os, and Pt nuclei around neutron numbers N≈90-94 reveal a quantum phase transition from a seniority-conserving structure to a collective regime as a function of neutron number. Although a system governed by seniority symmetry is the only theoretical framework for which such an effect may naturally occur, the phenomenon is highly unexpected for these nuclei that are not situated near closed shells.