What are the fundamental reasons that suggest us to minimise transmission power for energy-efficient radio link design? My question in short: 

Under which scenarios minimising transmission power is beneficial in terms of transmitter energy-efficiency? is there any fundamental reason to keep a low-power oriented design strategy?

In particular, small, low-cost transceivers (such as those used for M2M/IoT communications) are designed according to this strategy. I'd like to understand why.

Background

It is quite natural to think that energy efficiency in radio link design is directly linked to a low transmission power. This, however, cannot be concluded from a simple analysis (see baseline model below). For instance, we may feel tempted to decrease the data rate in order to reduce the required transmission power. This in turn increases the transmission time, and the total energy consumed does not change.

Naturally, this question requires a look to the whole transmitter circuitry (which is a little outside my field). After some research, I noted that there must be a trade off regarding clock rate (high-precision and high-rate is payed with extra power) and amplifier efficiency (lower input powers are usually less efficient). But this suggests that minimising power is not always the best option. 

The baseline model (optional)

Consider a wireless radio system where a transmitter $A$ wants to communicate with a receiver $B$, at distance $d$. The total attenuation (due to to signal propagation) can be simply modelled as $L=d^\alpha$, where typically $2 \leq \alpha \leq 4$. 

The carrier-to-noise density ratio $\frac{C}{N_0}$ at $B$'s receiver input is

\begin{equation}
 \frac{C}{N_0} = \frac{P_t G_A G_B}{d^{\alpha}N_0},
\end{equation}

where $P_t$ is the power at the output of $A$. When designing these systems, there is usually a performance constraint expressed as a maximum tolerated bit error rate, which turns into a minimum $E_b/N_0 = \gamma_0$ requirement.

So in order to achieve this $\gamma_0$, it seems that there are only two system design parameters to play with (assuming all other parameters are fixed): transmission power and data rate, i.e.

\begin{equation}
 \gamma_0 \propto \Big( \frac{P_t}{R_b} \Big).
\end{equation}

Thus, we observe that increasing the transmission power has the same effect that decreasing the data rate,  in terms of $E_b/N_0$. 

Now consider that the total amount of data to be delivered is $L_b$. The total energy consumed by $A$ to deliver $L_b$ bits is therefore

\begin{equation}
 E_t \propto  P_t\frac{L}{R_b}=\gamma_0 N_0 L,
\end{equation}

which does not depend on the operating power neither on the data rate.
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.