That, my good sir or lady, is a magnificent question, and truly worthy of a 'Frequently Asked Questions' reply, because it is, indeed, one of our most frequently asked questions.
The answer is based in how people use Triggertrap products. In general, it is one of two different uses: Very, very high speed photography, or very long duration photography.
High speed photography
By 'high speed photography', we mean things like capturing popping balloons, lightning strikes, and water droplets. These are events that are very quick indeed, and we are spending a lot of our time working to reduce the delay every step of the way. On Triggertrap Mobile, for example, we measure it in tens of milliseconds. On our older, Arduino-based products, we measure the speed in single-digit milliseconds.
The shutter lag on a SLR camera tends to be between 70-200 milliseconds. That means that when we trigger the shutter, there's a significant delay between us sending the signal, and the shutter triggering. To put that into context, a typical 9mm bullet travels at around 380 meters per second, which means that with a 100 millisecond delay, the bullet travels 38 meters (that's around 125 feet). Obviously, you aren't going to capture that bullet.
Even very fast Wi-Fi or Bluetooth triggering introduces a significant additional delay, which we don't really think is acceptable.
Long duration photography
The other side of the Triggertrap coin, is timelapses and sensor-based photography. In this case, we don't really care that much about speed, just about consistency. If we trigger every 3 seconds, for example, it's OK if it triggers 100 milliseconds late, as long as it does that for every single shots, so the interval between the shots is consistent, and the timelapse comes out nicely.
In the case of timelapses and other, slower sensor triggering (say, facial recognition triggering), the big challenge is battery life: We don't want to run out of battery. On most cameras, we achieve that by letting the camera go to sleep. When we want to trigger it, we wake the camera up, trigger the photo, and let the camera go back to sleep. This means that a normal SLR camera can last for ages on a single battery, especially if you set the camera up so it doesn't turn the LCD display on to preview the photo after every shot.
However, if we shoot with a wireless tether (whether that's via Wi-Fi or via infrared), the camera has to be turned on the whole time, 'listening' for the trigger signal. Without being able to go to sleep, it means that the batteries are drained very, very quickly. That works for a very select few types of photography, but not for one of the most common uses for Triggertrap products: Timelapse photography.
So, why the cable?
The cable solves both of these problems - Cables may seem a little bit low-tech, but they are extremely reliable (i.e. they either work or they do not), they are much, much faster than using a wireless connection, and it means that the camera can turn itself off for most of the time in long-duration modes.
Unfortunately, this state of affairs is pretty frustrating to people who have cameras that only have Wi-Fi or IR remote triggering, but we believe that this is a silly choice from the camera manufacturer, and a shortcoming on the camera: Without a good wired remote port, the camera isn't suitable for high-speed or long-duration photography.