The example given by OP shows he doesn't have proper understanding. The fact is that the failure of engine does not cause increase in LDR. It's only when there's addition to Vapp then LDR increases. And with OEI it only happens when there's ice accretion on wings and it's not possible to symmetrically deice because the crossbleed has to be shut(due to whatever the reason). So for better control there is addition to approach speed which increases the landing distance.