Why are GND pads often only connected by four traces?

This is to make soldering easier. Those 4 traces make it easier for the pad to heat up as the heat can only escape through those 4 traces. Soldering to a GND pad is difficult enough as it is, but if you had none of the spokes, you would essentially be trying to heat up the whole ground plane. It would be exceptionally difficult to heat it sufficiently to solder.

There may be some other reasons too, but this is the one that I know of!

As pointed out by @John Go-Soco in the comments, these are also reffered to as thermal reliefs

It's worth mentioning that for reflow processing, thermal relief doesn't matter. The oven will take care of heating it. But for prototyping it becomes real PITA to (de)solder the pads.

That connector is an SMT connector. The thermal reliefs make the pads much weaker so it doesn't take that much vertical strain to peel them off the PCB. For mechanical strength it's better to leave the mounting pads as full contact, I don't think I've ever broken off an SMT connector that had solid copper on mounting pads.

They are commonly referred to as 'thermal relief', and as others state, they are to make soldering easier, as they impede thermal conduction to the rest of the ground plane. The thermal conductivity of metal is, like electrical conductivity, determined largely by the free electrons. So beware, this also impedes electrical conduction.