What are the fundamental reasons that suggest us to minimise transmission power for energy-efficient radio link design?
Note that there are a host of practical secondary effects of increasing transmission power that do not scale with potentially less required transmission time, such as: battery impedance, voltage converter startup time, oscillator stabilization and carrier synchronization time, leakage or resistive losses due to larger required transistor sizes and/or higher voltage capacitors, more EMI shielding due to any higher digital edge rates required for processing, antenna shielding/spacing to limit human RF exposure, larger required heat spreaders/sinks, and etc.  The goal is often to minimize, not transmission power, but all these secondary power losses or inefficiencies, and/or their associated device costs, assuming some lower bandwidth or latency of delivering messages meets design goal targets.