12 pins for power 4 pins to tell the GPU how much power it can safely draw, 150/300/450/600
The connector/power design itself is a problem but that is only on the high end cards. 600W is a lot to ask of a cable rated at 675W, any defect is multiplied. What most of the big cards lack is current sensing on the pins. They treat all six 12V wires as a single bus. If one wire has higher resistance, it will take more of the load and this can have a cascade effect as it heats up until the point of failure.
The included adapter should be fine.
There should be 5060Ti models that don't use the 12VHPWR cable if you really don't want to mess with it. You could also get an ATX 3.0/3.1 PSU with the cable and just use that directly.