I'm surprised no one's made a topic for this yet.
The recent SDA speed run clocks in at 4:26, but I believe a sub 4-hour run is certainly possible as a TAS. The strategies the Speed Runner used seemed pertty solid, and I was impressed he managed to avoid any damage at all, which must have taken a lot of practice.
Avoiding all unnecessary 'normal' battles and only getting EXP from bosses gives you all you need to finish the game. Save for the few enemies you have to fight in the Stardust Fields to get coins, and in the Desert Valley to keep the Princess from being kidnapped. There is one change, though, that I still can't decide if it would be worth doing. Getting enough Beans to get the Great Force item, which doubles the damage given and recieved by the Bros. Recieving damage is a non-issue since you'll be dodging everything. However there aren't a whole lot of /long/ battles where doing double damage would pay off, compared to the time spent getting it. You need to obtain four different 'coffee' drinks in order to get the Great Force. It's not likely that playing the Border Jump game to get 15 more Hee Beans, digging up 15 more Chuckle Beans, and manipulating enemy drops to get 30 Woo beans would be worth the time saved getting the Great Force, but it's something to think about.
It may also be possible to manipulate luck so that you get the 'Advance' version of Bros attacks faster, but I'm not sure how much that can be altered.
Buying armor is totally unnecessary, save for the #1 Trousers. The defense isn't an issue, but being able to strike first in battle is. In this department, the speed run had it good. Though he had loads more Syrups than he needed at the end of the game.
With correcting all the little errors throughout, a sub-4-hour run is certainly possible. Someone (more experienced than me) should certainly give this a shot, and it'll look nice next to Super Mario RPG. :>