I think boost converter will be a more correct terminology than boost inverter as it doesn't convert DC to AC.
Boost converters are used in electric vehicles to boost the DC side voltage to the desired value.
Boost converter with inverter is used in solar farms where the DC side voltage after connecting many solar arrays is boosted to required DC side voltage. This boosted DC voltage is then used with PWM switching to get the rated ac voltage.
In a two stage PV system consisting of a dc-dc boost converter and a an inverter, the efficiency is affected due to an increased number of components. Using a single stage boost inverter could contribute in improving the efficiency.