Why is a reduction in lift called 'drag'?
Induced drag is unrelated to leaking and vortex creation. It exists even in a wind tunnel where the wingtips touch the walls and thus prevent leaking and vortices.

Then what is induced drag? To create lift, the wing needs to be at some angle with respect to airflow (or be asymmetric), so the force vector points mostly upwards but also somewhat aft. Forces that point aft are generally called drag. Induced drag is thus a 'real' drag, not a reduction in lift.