With 0 CYA: if you start your day at 0 FC and add CH to get to a FC of 5. Say every hour you lose 1 PPM to oxidizing whatever. After 5 hours, you reach 0 ppm and now things can multiply freely. (Question: assuming a constant addition of bacteria every hour, does the kill rate/usage rate stay constant at 5ppm down to 1ppm? Or does the oxidation rate change depending on the PPM level in this 0 CYA scenario)
We usually reserve "CH" to mean Calcium Hardness though clearly from your context you mean chlorine (perhaps using "Cl" for that is a better shorthand?). What you wrote isn't true because the FC level need not go to zero for pathogens or algae to grow. It just needs to get low enough to not kill faster than they can reproduce at which point they will grow faster and also deplete the chlorine faster. Now in practice, the FC level with no CYA that is needed to prevent green and black algae growth is only 0.06 ppm so calling this zero is not unreasonable though in practice it is not possible to maintain such a low chlorine level everywhere in the pool. As for the constant addition of bacteria every hour, that has more to do with properly maintaining the FC level so that you do not run out. So long as you maintain an FC level that kills faster than the pathogen can reproduce, it doesn't matter how quickly the bacteria are added to the pool. You just need a chlorine feed system that can maintain the FC level because the FC level would otherwise drop faster when more bacteria are added more quickly.
In other words, you need to distinguish between the instantaneous chlorine concentration vs. the rate at which that chlorine concentration is maintained by adding more chlorine. Those are two different things. It is the instantaneous chlorine concentration that determines the chlorine kill rate of pathogens. It doesn't matter how much you have in reserve (though with no CYA there is no reserve unless you count the hypochlorite ion as reserve).
So this analysis is why in commercial/public pools with higher bather loads one must have chlorine measurement systems (be it automatic electronic or regular manual testing) along with fast responsive chlorine dosing in order to maintain an appropriate FC level. For the situation you gave with no CYA, pathogens and algae are not a problem because in effect the pools are over-chlorinated. Their active chlorine level is far too high. This higher concentration of active chlorine is mostly just oxidizing swimsuits, skin, and hair faster and creating disinfection by-products faster. As you point out in your subsequent post, 5 ppm FC with no CYA would be horrible. Most commercial/public pools with no CYA (usually indoor pools) have around 1-2 ppm FC. There are plenty of commercial/public pools that use CYA but they are mostly outdoors. The pool industry doesn't understand CYA's significant moderating effect on chlorine so they end up over-chlorinating in all pools that have no CYA.
Europe has a much better understanding of this with the German DIN 19643 standard that doesn't use CYA but has a lower 0.3 to 0.6 ppm FC level and an even lower 0.2 to 0.5 ppm FC level when an ozonator is used.
With 50 CYA: you start at 4 and add CH to get to 9. Same amount of active (or, above saturation?) FC (5ppm) as the above scenario. So 5 hours later, your FC is at 4 and now the stuff can start growing, but not totally freely. The remaining 4ppm of CH will still get used up killing off things, but because the active concentration is lower than it was when FC was above 4ppm, it can't keep up with algae growth, and can only slow it a bit. (if this is true, then the "front line of soldiers" at 4ppm has fewer soldiers than the front line of soldiers at 9ppm. Right?)
You are incorrect about assuming the same amount of active chlorine as the previous scenario. It's night and day different. 5 ppm FC with no CYA has over 27 times higher active chlorine than 9 ppm FC with 50 ppm CYA. This is again why you need to completely divorce yourself from the idea that the FC level alone means anything other than the capacity or reserve of chlorine to not run out (i.e. a chlorine buffer). It has absolutely nothing to do with the active chlorine level as a number by itself. You have to additionally know the CYA level in order to know the active chlorine level (and also know the pH, though with CYA this isn't as important). Until you get that concept, you will be stuck thinking that FC means something.
For the soldier analogy, you are too focussed on the number in reserve (i.e. the FC). If you do not have enough front-line soldiers (active chlorine concentration) compared to your enemy, then they can kill your soldiers faster than you can kill them and they can overrun your lines. Furthermore, they can reproduce and grow in population. Sure, you may have lots and lots of soldiers in reserve, but what good do they do? The inadequate number of front-line soldiers are just a minor annoyance to the enemy who reproduces and increases in population faster than your front-line soldiers are able to kill them. You really need to get the idea of the reserve (FC) being that useful out of your head. It is ONLY important to have enough to get too low too quickly (i.e. before you next add chlorine), but they are not helpful in determining whether you will knock out the enemy.
In your 50 ppm CYA example, you are assuming that 4 ppm was too low but 4 ppm FC with 50 ppm CYA is enough to prevent green and black algae growth so it is not too low. That chlorine level still kills algae faster than it can grow. You are correct that at a constant CYA level having 4 ppm FC has fewer front-line soldiers than 9 ppm FC -- it's roughly 4/9th as much. Remember that the FC/CYA ratio is proportional to the active chlorine level so the concentration of front-line soldiers. At constant CYA, this means the number of front-line soldiers is proportional to the FC level, but again only for a constant CYA level. 3 ppm FC at 30 ppm CYA has the same number of front-line soldiers as 6 ppm FC at 60 ppm CYA or 10 ppm FC at 100 ppm CYA.
But then, adding the sun shielding effect, all the CH that was held in suspension with CYA was not degraded by the sun until it was released to active status, so the overall loss rate due to sun exposure is lower. plus, I think CG mentioned that the CYA might also have a sunscreen affect that prevents UV from penetrating deeper into the water, which would save the active/unbound FC from sun degradation as well, which is why you get better degradation rates at higher CYA in a not-totally-linear ratio.
The chlorine bound to CYA may also degrade in sunlight, but at a much slower rate than the chlorine that is unbound. In addition, CYA or possibly chlorine bound to CYA may block some UV from lower depths without degrading. Both of these factors together are why chlorine lasts so much longer in pools with CYA than without. The second effect is also why pools at higher CYA levels even with proportionally higher FC levels (so the same active chlorine level) lose less absolute FC per day.