If I we're into nit picking terms, the POH for the Piper Cherokee Warrior II lists several type of pumps in its system; no boost pump but 45 mentions of "electric" pump. Many of these were explanations of how you could diagnose issues, so a POH is well well worth reading.
The name itself is not the issue; I was using it to get people's minds off it doing a "BOOST" job in this category where it is used as a backup system for the failures you describe.
What the OP and several others were taking about was a boost pump to boost pressure.
Rotax and Jabiru engines have been developed for the upper end of the RA class doing much the same job as the entry level GA.
However what to OP is talking about is boosting pressure and reading a flow gauge and drawing conclusions.
Brendan has just given a good example with his XAir or what can be fitted to RA airctaft, where the basic engine had a hand operation redundancy pump, and it's been fitted with an electric pump. These pumps are supposed to fill the supply line then stop when the basic conventional carb float valve closes. In this class of aircraft, which can have all sorts of engines including Harley Davidsons, and with conventional car carburettors with a float bowl and float valve, it can be a a long process to adjust the shut-off leverage to get that valve closed against the pressure of the electric fuel pump. Thats a PRESSURE problem.
In terms of saving money by not using too much "boost" FLOW in the cruise on the above system at cruise is controlled by the main jet(s). You don't flirt with reducing jet size because you're only a whisker away from combustion chamber failure of valve heads, broken pistons and seizures, so no savings here. What's more likely is Brendan's experience, the electric pump hasn't cut out and is pumping fuel out of the Carb overflow, hopefully into an open-bottom engine compartment. When you turn the pump off the fuel "burn" per hour get's better.
Since, if you know fuel burn at cruise for your engine at a decimal point per hour (not per Nm), you will immediately diagnose a fuel puymp cut off problem. If you have been practising the basics of electric pump control you probably won't know there's a problem unless you have a closed engine compartment and there is wet fuel or stain at the bottom.