A while back I did some work by another forum member to incorporate an interesting chip with Raspberry Pi's. It really lacks a "PC" like start/stop button, but this was left out most likely for cost reasons. There have been many designs made to solve this challenge.
Linear came up with a couple of chips that helps to solve this problem, and with the help of the Raspberry Pi foundation, an overlay was created to get a GPIO port that can signal the end of the Halt status.
Based on that work, I created a design that is well documented and rather easy to build. While I was at it, I came up with a couple more designs that uses this chip, the LTC2951-1, although there are several in this family. Unfortunately, these chips are hard to get, not in-expensive at about $5 each, and come in a tiny, very tiny SMD package. On top of that, MOSFET's are used to switch the power, and the right ones (with a low RDS-on) are also only available in SMD packages.
Eventually, I was able to come-up with yet another design that is even more simple, and only uses 4 resistors and 1 capacitor, in addition to a push-button.
Here is the link to the posts on the Raspberry Pi forum:
https://www.raspberrypi.org/forums/viewtopic.php?f=37&t=128019
Enjoy!