Aviaton Engineer ?

nope - This kind of question tho is simply a logic question - No math required.
As for other answers about speed etc.. sure if you maintain speed then lift goes up- but that requires more power doesn't it.
So the flap does not increase lift but-it increases drag as it reconfigures the lifting plate (wing).
It is of course useful -applied correctly.
Flaps only exist because most full scale aircraft are simply a collection of compromises
Not enough power and too much weight
If weight could arbitrarily be changed and power were infinite -during flight - there would never be a need for flaps .