Running a pool without CYA is requires only a very small amount of chlorine for disinfection. Higher amounts will be very harsh, as explained above. The problem is, that when using the pool, this chlorine can be consumed very quickly. Just a pee-accident, and your FC is gone. To run a pool without CYA, you need a constant monitoring of your FC and constant adaptation of your chlorine production. Otherwise, you'll have to run higher FC to have a buffer to keep the pool chlorinated when using it, and to accommodate UV-losses, but without CYA, this extra FC will be very harsh.
With CYA, most of the FC is bound to CYA, where it is protected from UV. Only a small fraction is available as active HOCl. That's why the same FC with CYA is less harsh compared to a pool without CYA. When active chlorine gets consumed by UV or to kill pathogens, more active chlorine gets released from the CYA reservoir. With CYA, you need a higher FC level to always have enough HOCl at all times (that's where TFP's FC/CYA tabele comes from) - but you won't have too much HOCL, your buffer-chlorine is bound to CYA where it is not aggressive, but can get released quickly when active chlorine gets consumed.
IMHO, it is impossible to run an outdoor pool without CYA and keep it sanitized and free from algae at all times without an automatic FC measurement/control system. And even with a system like that, I would still recommend the use of some CYA (Some of these systems measure ORP, not FC. These systems don't really work well with higher CYA-levels, but that's another topic). And even indoor-pools, especially with higher bather loads, benefit from some CYA.