In the old days, why didn't aircraft use simpler systems to land on a Carrier? In the old days (during and before WW2), Carriers used arresting wires to help aircraft land. In fact this is still used today for jet-based carriers, but I want to ask about the old days with piston-prop aircraft because they go slower and generally make this easier.

I'm pretty sure even back in WW2, most carrier aircraft had tailhooks that grabbed the wire. This is so you "brake in the back", not the front. If you braked in the front, you are much more likely to nose forward or spin around.

Well, I've seen plenty of footage where that happens because something in the front of the aircraft, the nose or front wheels, gets tangled up in those wires, causing bad accidents. Here's a good compilation that has all sorts of landing accidents, including with the wire. What tends to happen is the wire is snagged wrong and the aircraft nose dives into the deck, wrecking the propeller, and/or the aircraft goes spinning around.

I can think of several alternatives to an arresting wire:


Reverse Pitch Propellers (reverse thrust)
Powerful Brakes in the rear wheel, or all wheels
Drag Chute
Air Brake


To me the simplest solution seems to be the last one, an Air Brake. I've seen this on modern jets like the Su-27 (@ 5:06). It's basically a big flat panel that swings out and creates enormous drag. In the Su-27 they keep it near the center of mass so it doesn't induce large torques, but you can put it in the rear half of the aircraft too. That will "brake in the back" and I think it won't require any more airframe strengthening than a tailhook, since that brakes in the back too.

So why not use this simpler solution? For reference, an Essex Class Carrier has a runway of about 260 m. I actually could not find normal "landing distance" that a small aircraft (bf 109, spitfire, etc.) needs once it touches down. If someone can find that, we would be closer to an answer.
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.