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Enhanced octupole collectivity is expected in the neutron-deficient Ge, Se and Kr isotopes with neutron number $N \approx 40$ and has indeed been observed for $^{70,72}$Ge. Shape coexistence and configuration mixing are, however, a notorious challenge for theoretical models trying to reliably predict octupole collectivity in this mass region, which is known to feature rapid shape changes with changing nucleon number and spin of the system. To further investigate the microscopic configurations causing the prolate-oblate-triaxial shape transition at $A \approx 72$ and their influence on octupole collectivity, the rare isotopes $^{72}$Se and $^{74,76}$Kr were studied via inelastic proton scattering in inverse kinematics. While significantly enhanced octupole strength of $\sim 32$ Weisskopf units (W.u.) was observed for $^{72}$Se, only strengths of $\sim 15$ W.u. were observed for $^{74,76}$Kr. In combination with existing data, the new data clearly question a simple origin of enhanced octupole strengths around $N = 40$. The present work establishes two regions of distinct octupole strengths with a sudden strength increase around the $A=72$ shape transitional point.