It's important to understand the meaning of live in this context: The meaning of live is to preserve itself (and re/pro-create). Depression is a reaction to that this goal might not be reachable: Depression is putting you into an alert-modus, so that you work hard on fixing these/whatever (very tough) things to get back on track.

Depression stops you from doing things, it doesn't make you work on anything.

This isn't true at all.

Depression stops you doing anything. It sucks all your energy and leaves you unable to get out of bed.

You seem to be arguing it is analogous to some kind of immune response. It's not and there is no evidence supporting that.

I guess this is a case of arguing by definition. Depression is an illness in as much sleepiness is an illness.

That's completely incorrect.

Depression is a harmful state that the body may not be able to correct on its own.

Sleepiness is part of the natural circadian rhythm.