Plasmons in two-dimensional electron systems (2DES) feature ultra-strong confinement and are expected to efficiently mediate the interactions between light and charge carriers. Despite these expectations, the electromagnetic detectors exploiting 2d plasmon resonance have been so far inferior to their non-resonant counterparts. Here, we theoretically analyse the origin of these failures, and suggest a proper niche for 2d plasmonics in electromagnetic wave detection. We find that a confined 2DES supporting plasmon resonance has an upper limit of absorption cross-section, which is identical to that of simple metallic dipole antenna. Small size of plasmonic resonators implies their weak dipole moments and impeded coupling to free-space radiation. Achieving the 'dipole limit' of absorption cross-section in isolated 2DES is possible either at unrealistically long carrier momentum relaxation times, or at resonant frequencies below units of terahertz. We further show that amendment of even small metal contacts to 2DES promotes the coupling and reduces the fundamental mode frequency. The contacted resonators can still have deep-subwavelength size. They can be merged into compact arrays of detectors, where signals from elements tuned to different frequencies are summed up. Such arrays may find applications in multi-channel wireless communications, hyper-spectral imaging, and energy harvesting.