It all still applies even to single GPU cards, but no where near as bad, as the power drain will lead to higher temps inside PSU (and now for the sciencey bit), and the higher draw of power will strip the electrons from the copper (and other elements and substances used) at a quicker rate, even more so with the higher temps which in turn leads to what is commonly known as component degradation, and that is without the damage that will eventually come with running the PSU near its rated limit continuously (can lead to the capacitors to burst due to heat expansion inside them which is where the lids pop), diodes to break (passes current both ways instead of one way, and they are used in converting AC / mains electric (a bridge rectifier) to DC), resistors to turn into light bulbs (with an accumulation of dust inside PSU, with any of the above, can lead to fires).
Yes I realise that what I have stated above, is just the basics and the fire thing isn't a high probability with todays better quality components (but the risk is still there), but it should hopefully give you a basic insight into why the long term isn't a healthy option.
The single cards still have the above but at a lesser rate as they are drawing much less power, therefore generating less heat and pulling less current so they are doing so at a much slower rate, and surface mounted components (the little things on circuits) are much more prone to heat as they haven't the volume or surface area to dissipate the heat as effectively.
Hope this kinda of helps explain things a little.