Octane and the burn curve aren't necessarily related. High compression engines need higher octane and also typically operate at higher RPM ranges, which requires a faster burn...

You'll find that fuels have varying Reid vapor pressures that will help with intake charge cooling more than others, which may help increase power via better atomization/distribution. A lot of stock eliminator guys will typically run C11 or C12, and those engines have less than 10:1 compression and huge cams that produce low cranking compression. Some fuels like hot vs cool engines (or hot intake charges from boost).

That being said, many people use race fuel for consistency in tuning run to run (or class rules) even if the engine doesn't require it. I have a big block iron headed engine here with 10.5:1 compression that doesn't care whether it's on pump or C12 (it actually picked up a tick on pump on the dyno). My stock 440-6 has some preferences that show up on the dyno in terms of fuel, but it's maybe 5 hp difference.

Pump gas is inconsistent but also oxygenated, which can help make power. You may also find that race fuel has lower specific gravity than the pump gas you're running, which means you need to jet up to get the same power input.

Overall - fuel testing and tuning takes a lot of time and effort. It's definitely not as simple as the guy at the cruise night spouting off "yeah she really runs good with the race gas!"