We expose the limitation of modular multilingual language models (MLMs) in multilingual inference scenarios with unknown languages. Existing evaluations of modular MLMs exclude the involvement of language identification (LID) modules, which obscures the performance of real-case multilingual scenarios of modular MLMs. In this work, we showcase the effect of adding LID on the multilingual evaluation of modular MLMs and provide discussions for closing the performance gap of caused by the pipelined approach of LID and modular MLMs. Multilingual language models (MLMs) suffer from the capacity limitation problem known as the curse of multilinguality, which penalizes the efficiency of MLMs, both in terms of training and inference, for acquiring new languages. Prior works (Pfeiffer et al., 2020; Ansell et al., 2021; Pfeiffer et al., 2022) alleviate the inference inefficiency bottleneck of the curse of multilinguality by introducing modularity in MLMs through language adapters.