About the old ideas, you are right. However, I still think that grad students actually make good reviewers in that the (good) ones have a keener sense of what is bullshit (as in "this suspiciously missing control is not suspiciously missing: you were afraid it would disprove your oversold message").
But yes, supervision is useful, because there is value in experience. BTW, when I say "grad students" I mean students vying for PhDs who already have at least a master's degree. It is a bizarre (to me) Americanism to call grad students people with only a bachelor.
If find it a bit sad that you think that students will steal ideas from the papers they are reviewing. On the other hand I find it heartwarming that you have students good enough to scoop papers already in review