@OP: I'm not saying your opinion's wrong or anything, but you missed quite a bit:
1. You absolutely don't have only ten extra rounds in the opening house. There are two extra clips to the right of where you enter, and two near the door you barricade. There's also a barrel that randomly has either money, shells, or more pistol ammo, and a grenade hidden under the melons on the table.
2. The executioner's not as difficult as he looks. He's hard, no doubt, but you have a much better chance (and the fight is much more fun!) if you run outside as soon as he enters. There are lots of places to climb, tons of items (including an SMG), explosive barrels galore, and plenty of tactical opportunities. Also, it just takes three shots with a shotgun or sniper rifle to knock him down so you can go in for an uppercut. If you've been trying to fight him simply inside the starting house, you'd have much more trouble than Capcom intended for that fight.
Hope that helps