As you wish. Let me be frank then.

At first level, the ability to hit twice for half damage is much better than the ability to hit once for full. After all, at first level, the dice play a much bigger "roll" in determining whether you beat an opponent's AC. To use your example (which was incorrect), two melee fighters, one a battle monk and one a fighter, attack the same opponent. They each have +5 to hit, (18 Str and +1 BAB), and the opponent has 4 HP and 14 AC.

The fighter has a 55% chance of killing the target. The monk has a 55% chance of killing the target, two times in a row. Damage isn't nearly as important at first level as hit chance is.

Edit: This is why Two-Weapon Fighting exists (And requires a feat to even use, as opposed to sword and board or two-handed). In the first few levels, extra attacks will almost guarantee you to hit and a hit is pretty much guaranteed to kill. (With high enough Str)

The monk doesn't have an off-hand, so TWF's normal -2 penalty on both attack rolls and half Str on the off-hand attack (WotC's intended balance point) do not apply. The monk is able to be twice as likely to kill as any normal warrior because he relies less on luck.
chech the warblade

now check steely strike, an ability warblades can do at level 1

The warblade is the balance point for this attempt at fixing the monk.

the warblade is, out-of-the-box, somewhat even with fighters and barbarians (and better that PHB monks) in raw damage, and way better that the aforementioned in versatility.

My point with all this is: This class is supposed to be out-of-the-box better than 2 weapon fighting fighters and PHB monks.