Personally, I'd contend that you get the fast exposures because you have a bunch of light-gathering, not because you have a lower focal ratio. I learned early on in astronomy that it was the focal ratio that mattered and it took a while to get that beat out of me - and seeing some fast acquisitions of targets at rather high focal ratios was rather confusing.
Assuming the same aperture, if your target (presented in the image circle) fits on the sensor you should be getting exactly the same amount of light hitting the pixels of your sensor whether your focal ratio is 2 or 10. You get the same amount of signal. Read noise is diminished by using the faster focal ratio but with a modern (especially cooled) low-noise CMOS sensor your read noise is not high enough to be a real bother for most of us and could be considered negligible.
Historically a camera lens would change its effective aperture (using the old iris) when one changed the focal ratio. It is very rare in DSO imaging that we stop down our optics so the choice of focal ratios does not involve changing the aperture and thus does not involve changing the amount of signal you are getting from the target.
With a system with a focal ratio of less than 4 you apparently actually start running into problems with the angle of the incident light on the microlenses of your sensor and start getting some reduction in the amount of light your sensor actually captures. At F/4 I understand it really isn't significant but at F/2 it is more significant and how significant may depend on the sensor and I think most of us would consider it to be acceptable.
In a good and fast camera lens they actually add straightening elements so that you can have a very fast focal ratio without a big reduction in the amount of light being gathered (and an increase in the amount being scattered) but so far as I know, our astronomical OTAs don't have straightener elements.