A binary neutron star (BNS) merger can lead to various outcomes, from indefinitely stable neutron stars, through supramassive (SMNS) or hypermassive (HMNS) neutron stars supported only temporarily against gravity, to black holes formed promptly after the merger. Up-to-date constraints on the BNS total mass and the neutron star equation of state suggest that a long-lived SMNS may form in $sim 0.45-0.9$ of BNS mergers. A maximally rotating SMNS needs to lose $sim 3-6times 10^{52}$ erg of its rotational energy before it collapses, on a fraction of the spin-down timescale. A SMNS formation imprints on the electromagnetic counterparts to the BNS merger. However, a comparison with observations reveals tensions. First, the distribution of collapse times is too wide and that of released energies too narrow (and the energy itself too large) to explain the observed distributions of internal X-ray plateaus, invoked as evidence for SMNS-powered energy injection. Secondly, the immense energy injection into the blastwave should lead to extremely bright radio transients which previous studies found to be inconsistent with deep radio observations of short gamma-ray bursts. Furthermore, we show that upcoming all-sky radio surveys will constrain the extracted energy distribution, independently of a GRB jet formation. Our results can be self-consistently understood, provided that most BNS merger remnants collapse shortly after formation (even if their masses are low enough to allow for SMNS formation). This naturally occurs if the remnant retains half or less of its initial energy by the time it enters solid body rotation.
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