Not all are bootstrap-capable, and many do co-generation for district heating, which can power absorption heat pumps for cooling in the summer.

Also a gas turbine core that's spinning can modulate power in seconds, unlike one that has to first be brought up to speed with external power (even if that's from batteries, or an on-site diesel (like AFAIK in the case of the black start capability of the downtown power plant in Wuppertal Barmen)).