When a capacitor fails it doesn't necessarily break the PSU. No protection circuitry will detect high ripple from a leaking or swelling capacitor. There is no such thing as "ripple protection". I think transient response may somewhat be affected by failing capacitors, but primarily their function is to filter ripple, so if they are failing and you have high ripple, that could dramatically decrease VRM lifespan of your GPU, motherboard, and hard drives without you ever realizing. If a lot of capacitors fail, then hardware might not even function, or could be damaged if somehow a protection circuit of the PSU does not detect it.
Capacitors can start to lose their charm even before they have any physical signs of failing. They don't need to be swelling, bulging, leaking, or vaporizing to be losing their capacitance; they can appear to be perfectly fine, yet your ripple will be going higher. My Toshiba television from the 90s has bulging capacitors when I look inside, yet that television still works. But the high ripple from those capacitors is not healthy for anything connected to that PSU.