Why hydro is not as flexible? A cable from Germany to Norway is being built to use hydro plants in Norway as energy batteries. This is despite Germany having natural gas plants.
Increasing capacity at hydro power stations or other baseload stations isn't as easy as just "putting a larger generator in". Everything needs to be considered and sized up: turbines, piping, outlets, new environmental assessments, etc., just as in any other type of power plant.
The current water level in the reservoir, expected drainage and rainfall over the year, environmental regulations concerning water discharge and intake levels, fish, etc. all play into it. Note that a hydroelectric power plant doesn't just generate electricity, it also regulates water levels pretty far up- and downstream from the plant.