As stated - focal ratio has not a thing to do with astro exposure time. It has everything to do with the TFOV. Photons are photons, and an electron volt is an electron volt.
A photon vs. well depth and energy - all that DOES NOT CHANGE - what does change is relative scale of image to pixel size... There is no possible way a photon somehow is 'more better' at one f ratio over another for A-P - they are boringly similar. To state that a fast ratio scope can image 'faster' than a low f ratio scope is just plain wrong. Imaging is about the pixel size relative to the f-ratio, it's a gaussion curve and efficiency depends on a LOT of things, not the least of which is the luminosity and desired resolution of the imaging target.
What becomes difficult at faster f ratios is the critical focus plane (and if using mirrors the collimation) and the dual speed focusers are very important on scope under f/6. What becomes difficult is also controlling field curvature in the focal plane at prime focus.. What becomes better is the maximum 'Total Field of View' (TFOV)for the given aperture. Sorry if it get's complicated but this also affected by choice of eyepiece FOV, or imaging chip and it's pixelsize/count.
Consider a focal ratio of f/7-8 as a sort of tipping point, or low center on a sort of pendulum function.
As the focal ratio gets smaller/shorter(lower F number) the 'potential for field curvature' increases (think of it as stressing the optic more per mm away from dead center) and the TFOV of the telescope optic increases.
As the focal ratio gets higher/longer(higher F number) the potential for field curvature gets smaller and the corresponding TFOV of the telescope optic decreases.
As a generality, longer focal ratios are more difficult to guide for imaging. This has a lot to do with the pixel size and 'arc second seeing' where you are, but also the greatly exaggerated relative scale definition of what is in the plane at prime focus.
From the point of projective geometry - think of it as a mapping function. A large TFOV will contain more 'information' at a lower resolution than a same aperture at a much longer (higher) focal ratio - which will have less TFOV but contain more resolution within that field. Fast(low f ratio number) a field corrected with a Field Flattener. High focal ratio scopes are field corrected (widened) with a Focal Reducer.
A notable exception to all this is the Petzval refractor desigh as seen in the TeleVue, Vixen, and Takahashi models. A wide flat TFOV is something some folks are willing to pay extra for? Edge HD and Tak FSQ, TV Paracor and Baader MPCC. There are others that try, but with added complexity 'can' come added difficulty in other ares.
Another consideration is in the visual use - eyepieces/magnification and exit pupil for a given aperture and object under scrutiny.. this a little more complicated by the fact that adding aperture cm's or inches and holding the f ratio constant will allow for a larger exit pupil at a desired size. Think of it as 'light cones' one extending from the telescope to space, and the other going from the eyepiece to your eye.
For visual astro think of it as the focal ratio tells you what the maximum TFOV of the optic is AND what eyepiece sizes will be practical for both magnfication and exit pupil. Design specific it tells you if a MPCC, ParaCORR, Focal Reducer or Field Flattener will impact the experience.
For astro imaging it tells you what the TFOV of the optic is and in turn what the arcsecond-seeing formula dictates as an optimal window for the pixel size of the CCD. Also if a Focal Reducer or Field Flattener will give advantage of flexibility - or mandatory.
I think focal ratio a more important number/concept to understand than the obvious aperture/light gathering often touted as king - and a great question to ask. It's all about light bending, but not about a photon somehow going faster or slower. Understanding focal ratio is fundamental to the overall experience for visual or imaging - and can help you buy 'smarter'.