@Walter I think your table may be in error, the currents you have listed are very low, assuming I am reading it correctly. A wire gauge (AWG) of 16 can handle way more current than 3.98Amps. Below is an example wire gauge to current capacity chart that may help:
The wire lengths for the 3D printer are relatively short, but don't forget that it is a round trip for the current, so 2x your length from the supply to the heater bed.
Regarding the need for an SSR of other switching device. It will not harm, but is not needed for 12v or 24v PS, as long as the current is kept within the operating specs of the controller's on board MOSFET. It is absolutely needed for 120 or 240v AC heated beds, the controller board is not capable of supporting such voltages. One of the nice things about going with a 24v PS is the halving of the current being drawn (compared to 12v) for the heated bed. This allows some increase of the heated bed wattage, and still not need an external SSR, MOSFET or relay.
Regarding safety, low voltage (for the sake of this discussion, let's just say < 24v) systems are considered in general safer than line voltage (with regards to injuring a person). This is why the safety standards are completely different for low voltage lighting. Someone can inadvertently become part of the circuit without danger of receiving a significant shock. Most of the time our skin is not moist enough to allow much current to flow, and therefore you don't even feel anything. One can not say the same for line voltage. This is not to say that using line voltage for the heated bed can not be done safely, it can, and in no way am I saying you should not use such heaters.
Please keep in mind though, novices are potentially building these printers. Anything that limits their exposure to potential shock from line voltages make it safer, even if only a little.
So, in general I would say that if you know what you are doing, you can make most things safe to operate, but if you don't get help. I will also add that with both low or line voltage, there is alway the potential for fire risk, and Walter is quite correct to point out that higher currents if not managed correctly, can lead to overheating of connectors and wire. No matter the voltage, be smart about what you are doing.