I have always used a large 12VDC power supply to power multiple scanners. In my tower build I had 2 dozen scanners and several accessories (multicouplers etc.) powered off a 25A Astron power supply. In my current slimmed down shack I still run that same Astron with 7 scanners, an Icom R8600, a dual bander and a GMRS radio, all with no problems.
I use PowerPoles, this makes it incredibly easy to connect and make changes. Proper fusing and staying within the limits of the power supply will help ensure proper operations.
Those 4-connector adapters mentioned above are fine as long as the power supply has enough capacity to run the devices connected to it. The issues
@sallen07 reported are probably due to initial voltage drop, the supply itself possibly had a bad voltage regulator and when the radios would all turn on at the same time it would fail due to that. If you have a voltmeter try checking the voltage to see if that is the case. (As an aside, those adapters were actually developed for surveillance camera use...) I have used the ScannerMaster adapter for running 3 scanners and a multicoupler and there was no problem, it is possible he got a bad unit or (less likely) one of his radios had excessive current draw.
WallWarts and other cheap power supplies often have poor voltage regulators and sometimes rely on the load itself to bring down the voltage to the proper level while more expensive supplies (line Astron's and Samlex) are more properly regulated.
I tend to prefer linear power supplies as they usually do not require fans for cooling like most switching supplies do. The fan noise can be distracting, even the ones that are are only on as needed.
Switching supplies are often smaller, lighter and cheaper but the fan noise bothers me. Newer ones are less prone to making RF noise and switching supplies had a bad rap in the past but newer and better ones (like the Samlex SM1325 I have) are no RF noise issue as far as I have seen.