Haters gonna hate
I can see a single rocket working better in many parts of the game, but there's a few spots I'm genuinely curious how you'll get by. The section after the bridge in level 5 for one, without being able to kill the guns behind the bunkers from straight on I'm pretty sure either of the little shortcuts will be unusable to you, and just getting through alone would be a bear (unless you're not powering back up until after that section). Another one that leaps to mind is the conveyor flanked by turrets towards the end of 6, unless rank's low enough that you can just charge the center.
I must admit this approach just seems wrong to me, but I can see benefits to it. Even if you're going low powered through the end, though, I'd still think being fully powered at the start would be beneficial. It's possible to get 3 POWs in the first level with taking barely any time out (I'd be surprised if you lost a whole second), and even with max rank the first few levels don't throw that much at you so keeping lag in check isn't too bad. The 4 (or at least 2) way spread really does help clear out enemies at the start of boss fights so you can get into position right away.
I must admit this approach just seems wrong to me, but I can see benefits to it. Even if you're going low powered through the end, though, I'd still think being fully powered at the start would be beneficial. It's possible to get 3 POWs in the first level with taking barely any time out (I'd be surprised if you lost a whole second), and even with max rank the first few levels don't throw that much at you so keeping lag in check isn't too bad. The 4 (or at least 2) way spread really does help clear out enemies at the start of boss fights so you can get into position right away.