In the old days, why didn't aircraft use simpler systems to land on a Carrier?
The benefit of a cable is that it's a mechanical means of arresting the aircraft. You either catch the cable and stop, or miss and go around. Aside from breakage and malfunction, there is no in-between. If braking is left entirely up to the pilot, it's up to them to engage all the right functions quickly enough, and in sufficient amounts. If they misjudge, they end up going into the water.
Cables are also effective at stopping aircraft quickly. This means less deck space is needed for landing, and with the introduction of the angled landing area, allows aircraft to be launched and recovered at the same time. Only a tail hook is needed to be added to the aircraft, which adds great braking effectiveness for relatively little weight. Other options have reasons they would be less effective than cables, with greater penalties in areas such as weight.
Reverse Pitch Propellers (reverse thrust)
This can be an effective way to help slow a propeller aircraft down. The downside is that it's up to the pilot to engage the reverse pitch and in a sufficient amount. Single engine aircraft can be hard to control especially if higher power settings are needed while in reverse.
Powerful Brakes in the rear wheel, or all wheels
Brakes are limited by the friction between the wheel and the ground. On carriers, this was generally wood, later replaced by metal. Especially when wet, this does not provide very much friction. Increasing downforce (see the air brake section) can help, but only to an extent. And as you noted, especially with tail draggers used on early carriers, aircraft would nose over if they braked too hard. The tail wheel doesn't have much weight on it, so would not be effective in braking.
Drag Chute
You'll notice that pretty much the only aircraft that use drag chutes are aircraft that land at high speeds and already need long runways. This is where you get the most benefit from a chute; long landing rollouts at high speed. As speed is reduced, they become less effective. You need to spend the time recovering, repairing/replacing, and re-packing the chute after each landing. They are also going to be less reliable than a tail hook. If it fails, you can't land on the carrier, you may just have to bail out.
Air Brake
Air brakes are similar to drag chutes in that they work best at high speed. While they are are not a consumable item, the drawback is that they have much less area, and therefore much less effectiveness than chutes. They work best when they can also provide downforce to improve braking friction, but still need high speeds and long distance to really provide benefit.
Carrier aviation in World War II was certainly dangerous. Many pilots died in accidents rather than in combat. But the military was still learning about how useful carriers would be in combat, and figuring out what the best configuration for carriers and their aircraft would be. Carrier aviation has come a long way since then, and cables are still the go-to system for recovering aircraft that don't at least have some kind of STOVL capability.