In the context of warped extra-dimensional models which address both the Planck-weak- and flavor-hierarchies of the Standard Model (SM), it has been argued that certain observables can be calculated within the 5D effective field theory only with the Higgs field propagating in the bulk of the extra dimension, just like other SM fields. The related studies also suggested an interesting form of decoupling of the heavy Kaluza-Klein (KK) fermion states in the warped 5D SM in the limit where the profile of the SM Higgs approaches the IR brane. We demonstrate that a similar phenomenon occurs when we include the mandatory KK excitations of the SM Higgs in loop diagrams giving dipole operators for SM fermions, where the earlier work only considered the SM Higgs (zero mode). In particular, in the limit of a quasi IR-localized SM Higgs, the effect from summing over KK Higgs modes is unsuppressed (yet finite), in contrast to the naive expectation that KK Higgs modes decouple as their masses become large. In this case, a wide range of KK Higgs modes have quasi-degenerate masses and enhanced couplings to fermions relative to those of the SM Higgs, which contribute to the above remarkable result. In addition, we find that the total contribution from KK Higgs modes in general can be comparable to that from the SM Higgs alone. It is also interesting that KK Higgs couplings to KK fermions of the same chirality as the corresponding SM modes have an unsuppressed overall contribution, in contrast to the result from the earlier studies involving the SM Higgs. Our studies suggest that KK Higgs bosons are generally an indispensable part of the warped 5D SM, and their phenomenology such as signals at the LHC are worth further investigation.