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Recent observations have confirmed that Gamma-Ray Burst (GRB) afterglows produce Very High-Energy radiation (VHE, E > 100 GeV). This highly anticipated discovery opens new scenarios in the interpretation of GRBs and in their role as probes of Extragalactic Background Light (EBL) and Lorentz Invariance Violation (LIV). However, some fundamental questions about the actual nature of VHE emission in GRBs and its evolution during the burst are still unsolved. These questions will be difficult to address, even with future imaging Cherenkov telescopes, such as the Cherenkov Telescope Array (CTA). Here we investigate the prospects of gamma-ray sky monitoring with Extensive Air Showers arrays (EAS) to address these problems. We discuss the theoretical aspects connected with VHE radiation emission and the implications that its temporal evolution properties have on the interpretation of GRBs. By revisiting the high-energy properties of some Fermi-LAT detected GRBs, we estimate the typical fluxes expected in the VHE band and compare them with a range of foreseeable instrument performances, based on the Southern Wide Field-of-view Gamma-ray Observatory concept (SWGO). We focus our analysis on how different instrument capabilities affect the chances to explore the burst onset and early evolution in VHE, providing invaluable complementary information with respect to Cherenkov telescope observations. We show that under the assumption of conditions already observed in historical events, the next-generation ground monitoring detectors can actually contribute to answer several key questions. [ABSTRACT FROM AUTHOR]