Easy to see for yourself sirs. Go get a high-compression car that says “premium gas only,” and fill it with 87 octane. Watch your power go through the floor as the ECU desperately retards the timing to keep the engine from tearing itself up 
Or get an older one without a computer that does that and listen to the pinging coming from under the hood
Is it a must in a modern high-compression car? No, I suppose not, as long as you’re OK with significant power loss as a result. Myself, if I just spent all that money for a whoop-de-do go fast car, I don’t want to be artificially slowing it down by putting lower grade gas in it.
And this is a good time for someone to insert the standard sermon: Higher octane gas does not = higher horsepower. If your car is designed for regular, putting premium in won’t turn it into a race car. Premium only has an effect on your power when you’re using it to prevent the computer from reducing power to avoid engine knock.