Of course not all engine failures on takeoff occur at V1. But it's the most tricky moment for it to fail
I would debate the conclusion of this statement. A/C on the ground only yaws. I used to give crews a wet V1 and create a V2 with space above Vr. You could see them anticipate the V1 bang; it didn't happen, then rotate, then bang as the nose came off and they sniffed V2. All said it was more 'interesting/entertaining'.
I was had my own check, B738. We were a crew of 2 TRE's renewing a type rating with a TRE from another company. He thought he'd 'educate' us. An NDB with F40, into GA F15 with engine failure as gear was selected up. Ref 40 +5 = V2F15 so our engine failure check was just legal and it was greatly entertaining and educational. Must better, realistic (Bird strike at 400') and educational in a/c handling than the usual wet V1 bang, keep it straight on the ground then rotate. However, I wonder at the failure rate of such imagination and the subsequent fall-out from the Ops dept to the Training dept.