The first main reason is strength, plastic standoffs used to be used commonly, but that is because the hardware of a computer was much smaller (Weird, huh?) and obviously less powerful, and with this less power, less cooling was needed to keep it within a temperature range. And the overall system (Not including the cases, they're like a tonne of bricks), was much lighter. And these days, metal standoffs are used due to the systems being much heavier, due to overclocking CPUs with heavy heatsinks and fans, the GPUs such as the Nvidia and AMD ones are much larger and more powerful, produce much more heat so more heatsinks and fans are needed to keep it cool.
If you didn't already know, the standoffs nowadays are made of brass, and therefore do not conduct electricity as good as other metals, like copper, so it works as a slight grounding technique as well as, to keep the motherboard off of the side of the case, which will conduct electricity, and basically short-circuit the motherboard and can damage the components.
Another reason, how often do you see plastic standoffs being used nowadays, and it is probably much worse for the environment (I couldn't really care
) rather than metal, which can be made much easier, and can be stored and found much easier.
There are probably other reasons, but this is what I think/see.