Sometimes I picture science developing some weapon of mass destruction based on the mechanics of Plato's Separate Realm of Ideas. Or is it "Ideals"? Or is it Greek, and therefore, neither? In any case, that whole Realm thing was one of those concepts I kind of instinctively rejected, but later kind of got into how it might work, like, on the level of Star Trek transporters, or Asimov's Laws of Robotics? - where you acknowledge that it's bullshit, but you still like to get in there and poke around, maybe accept the premise just to kick around the consequences a bit. See what fun stuff develops!
For everyday use, though, I think the primary place people still cling to to Platonic-style Idealism is when they start from a completely anti-logical, unnatural, human-invented concept (Perfection, anyone?) and attempt to "reason from it." As if one can reason from tinkerbell principles and expect to arrive at aeronautics. Reason from perfection? Shit, reason TO it first, see where that gets you. If you can pull that one off, then you can try reasoning from it once you get there, and see what it's actually made of.
Hm. "Anti-logical" is too strong. Perfection is not anti-logical (working contrary to), or even illogical (demonstrably in conflict with). How about "alogical"? Perfection doesn't occur in nature, and it's completely outside of anything logic can get you to.
The concept of "perfection" is a nonsense elevation of human aesthetics to some "as if" absolute principle of the universe, really.