Modern-day boilers, such as those in coal-fired power stations, are still fitted with economizers which are descendants of Green's original design.  In this context they are often referred to as feedwater heaters and heat the condensate from turbines before it is pumped to the boilers.
Economizers are commonly used as part of a heat recovery steam generator (HRSG) in a combined cycle power plant.  In an HRSG, water passes through an economizer, then a boiler and then a superheater.  The economizer also prevents flooding of the boiler with liquid water that is too cold to be boiled given the flow rates and design of the boiler.
A common application of economizers in steam power plants is to capture the waste heat from boiler stack gases (flue gas) and transfer it to the boiler feedwater.  This raises the temperature of the boiler feedwater, lowering the needed energy input, in turn reducing the firing rates needed for the rated boiler output.  Economizers lower stack temperatures which may cause condensation of acidic combustion gases and serious equipment corrosion damage if care is not taken in their design and material selection.