Why are modern digital cameras still stuck with the problem of shutter lag?

The iPhone has overcome this problem; incidentally, the iPhone's camera is terrible due to the amount of bright eye from the flash aside from the disgusting colour clarity.

A digital camera has to read the light pickup like a memory chip and store the information, this is slow with cheap cameras but the more expensive ones are faster. None are as fast as a traditional mechanical camera which takes a film.

There are multiple things that contribute to shutter lag and there are plenty of cameras out there with very little shutter lag, including many of those based on the same Sony camera module in your iPhone.

The two largest lag inducing issues are waking up the camera electronics, and focusing the lens. The advantage camera phones have over compact cameras is that they are pretty well permanently switched on. The time required to focus a camera phone though is a mixed blessing, they focus fast because they tend to use a wide angle lens with a deep depth of field. Great if you want a wide angle lens, but not so hot if you don't.

For now I'll stick with my 12FPS burst rate with continuous AF on my Sony SLT!

Modern dSLR cameras have always been faster than P&S.

The reason is that the dSLR is based upon a 35 mm SLR and the shutter lag is measured in milliseconds, even when using it in the program mode. The exposure and auto-focus are done independentely and thus the lack of apparent shutter lag

P&S cameras do all the thinking for the user and has to have the time for the camera to setup the exposure and auto-focus. If you press the shutter release half way down and then compose your shot, the shutter lag will be a much shorter time than if you don't… And remember, shooting using the onboard flash further slows down the time between each exposure

They're not if you use a proper camera!