Are fast lenses only fast when shot wide open?

Question

Given two lenses with different max apertures but the same size image circle (say, full frame on a Nikon FX DLSR camera) and taking shots at the exact shutter speed and focal length under the same lighting, taken on the same camera, say, f/1.8 and the other f/4.5, if I shoot the faster lens (the f/1.8) at an aperture of f/4.5 doesn't it let in the exact same amount of light as the "slow" f/4.5 lens?

In other words, do I have to have a narrower depth of field (and thus more demand on accurate autofocus) to get the benefit of the fast lens, or if I shoot with a smaller aperture and have more depth of field do I "lose" the speed benefit of the lens (i.e. letting in more light)?

Answer 1

In theory, both lenses will allow the same amount of light to pass through at f/4.5, so yes, when stopping down, you lose the advantage of fast lens. The actual amount of transmitted light depends on the lens design and is measured in T-stops.

But the fast lens will still make a difference when you look through the viewfinder and your autofocus will also gain from it as the lens is only stopped down to the aperture you set for the shutter actuation time.

Answer 2

Since the aperture isn't stopped down until the exposure is made, you get the benefit of:

1. A brighter viewfinder
2. Faster, more accurate autofocus.

Once the picture is taken, at, say f/4.5, you get the DOF that you'd expect.

Answer 3

I think the answer is: yes, faster lenses are only faster shot wide open.

In addition, based on this question it looks like it's possible that the faster lens may be also have a few other advantages:

1. sharper at other apertures
2. a brighter viewfinder (since it's wide open until you hit the DoF preview button) for low light situations

Can anyone find a reference for (1)? (2 seems fairly obvious)