There is no good answer, and I've always said there's not supposed to be. It was meant to be stupid and reckless, and it relied on luck to work, probably just like most of young Kirk's command style to that point (let's remember luck has always been a good friend of our captain). We're supposed to roll our eyes at it. It's like off-roading in your dad's Cadillac Escalade: fun, but irresponsible and a bit dangerous. A 35 or 45 year-old Kirk would've saved the planet too, but not that way.
Your analogy reminds me of the soliton wave from TNG. The wave was traveling at warp speed and was losing control, threatening to destroy the planet at the end of its path. The plan was for the E-D to catch up to it, overcome the wave, get in front of it, and then blow it up with aft torpedoes. But instead of going over or around it, the Enterprise went *through* it, causing a fair amount of damage to the ship.
The Enterprise was clearly faster and could change course to pass it by. There was even enough time between passing up the wave and destroying it to mount a rescue mission in the ship (which needed to happen because of the damage from going through the wave in the first place). But no, Picard said to charge right through.
So it makes no other sense than because it made for good action packed TV. And frankly, I think Picard yearned for a dune buggy ride on a desert planet.