Those connectors are supposed to be maximum 7A per terminal. 8 conductors is 4 pairs (what comes out one yellow wire loops back in a black ground wire) so that's 4x7 = 28A total, which at 12V would be 336W. That's the point you risk melting it, but I expect for most of us our cpu cooler will have given up before we hit the limit of a single 8 pin connector.
In case the internet lied to me about the current rating of that molex connector (the Internet is always right, isn't it?) a rough estimate is that the rather similar PCIe 8 pin PEG connector is conservatively rated at 150W, but one of the connectors is a sense line not for power delivery so you only get three pairs from the possible 4. So scaling the 50W per pair for 6 active cables an 8 pin connector should allow 200W.
So that single 8 pin connector should deliver 200W all day no problem, possibly up to 300W. Driving even the bigger Ryzen chips from an old 4 pin EPS connector should be possible, but peaks will be on the limit.
If you intend using PBO overclocking where the motherboard will tell the CPU that it can deliver an unholy deluge of power, then it might be wise to connect it all up so it isn't lying. But then most of us don't overclock.
OTOH, if you have two 8 pin power connectors then I think it would look nice to have them both in use. But then I drive a car that really doesn't need twin exhausts at the back