From a "what it takes to get a properly exposed image" this is true, but it's also true that larger sensor sites pull in more photons and will thus tend to have higher signal:noise ratios, and thus better low light performance (which you mention with respect to noise, but my point being that this is due in part to "letting more light in" and also due to less electrical-cross-talk as I understand it).
I don't think that's the right way to think about it (in the context of exposure). Think about:
The FF is gathering more photons as you say but they're being spread over a larger image sensing area.
That's a lot like how you can take an f/2.8 lens to start with, but if you put a teleconverter on it, it "becomes" an f/4 or 5.6 lens. Different mechanism, but those photons are limited and they get spread out.
The absolute light level per sensor area is nominally the same for full-frame and smaller sensors. Consider two lens FF, and m4/3 (2x crop factor)
Olympic 25mm F1.8 - Diameter 56mm, Filter 46 mm (filter area - 1662 mm^2)
Nikon Z50 F1.8 - Diameter 76mm, Filter 62mm (filter area - 3019 mm^2)
The equivalent full frame F stop of the m 4/3 lens is F2.5 (1/crop factor).
Thus the (1/4 of full frame size) m4/3 sensor receives the same light level per sensor area. (1/2 lens area and 1 less f-stop) as a full frame.
For the same number of mega-pixels (say 24 MB) each pixel on the full frame has 4 times the area, and can thus gather 4 times photons of the m4/3 pixel. This enables the Full frame to have a lower ISO for the same shutter speed.
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“I went to the woods because I wished to live deliberately...” ― Henry David Thoreau
The FF is gathering more photons as you say but they're being spread over a larger image sensing area.
I don't think that's quite the right way to think about it either.
Photons aren't being "spread out" - a bigger sensor is a bigger "net" to capture more photons, but the number of photons at any individual spot is the same regardless of how big the net is. A smaller "crop" sensor is really just a smaller photo - a cropped version of the bigger sensor's image.
Photo exposure is sort of like putting out a sheet of paper to measure how hard it's raining. The time it takes for the paper to wet out will be the same regardless of how big the sheet is.
The teleconverter makes your lens slower because f-number is a ratio of focal length over the diameter of the aperture in the lens, so if you make the lens twice as long but keep the hole in the middle the same size, the ratio gets cut in half. Since that ratio is used to determine how much time is needed for the correct exposure, you then have to double the amount of time.
Based on a little reading, it seems like a lot of the difference in noise levels between FF and crop sensors (APS-C, at least, not tiny phone sensors) has been engineered away.
But the OP was originally asking about exposure vs motion blur (or camera shake, which is motion blur), and I'm not sure he's even paying attention to this thread anymore.
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Go! Take a gun! And a dog! Without a leash! Chop down a tree! Start a fire! Piss wherever you want! Build a cairn! A HUGE ONE!
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(-bootpathguy)
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