But assuming he had to leave his Strength pretty low to manage it, he won't be very good at actually accomplishing anything.
That is simply not true.
If you go with a Dex monk (as I have) you take that into account. (Full Disclosure: the last time I did this, it was a Githzerai monk, but the principles remain the same for Monks with lesser Dex scores.)
1) You'll have the edge on initiative.
2) You emphasize your ranged attacks- Monks can use
spears, javelins, crossbows, slings, daggers, clubs, shuriken and grenade like weapons.
The last Dex-monk I built had a Quiver of Ehlonna as his first magic item. For many combats, he simply became artillery. Raining down javelins and firebombs on enemy spellcasters can be quite effective.
3) You will have more AoOs if you choose Combat Reflexes. With the right weapon selection, you'll get to use all of them, too.
Of the Monk's basic weapons, only the Longspear is a reach weapon. You'll be able to threaten at 10', and anyone who gets closer faces your Unarmed Strikes.
If you have access to the DCv1, you can take Pole Fighter (selected polearm treated as a monk weapon, so you can flurry with it), Unotrhodox Flurry (selected light weapon treated as a monk weapon, so you can flurry with it), and Ring the Golden Bell (unarmed strike can be used as a ranged weapon) as well as other choice feats.
I used a polearm with my Dex monk, and dealt out nearly as much damage per round as the party's Barbarian (due to AoOs), while my Dex & Wis combo gave me the best AC in the party.
4) You won't be hit as often.
5) You'll make more of your Reflex saves.
comrade raoul and I discussed the benefits and detriments of each build vis a vis each other in a thread last year. Swapping a 14 & 16 betwee the two relevant stats, on average, the Str monk dropped his opponent about a round faster than the Dex monk, while the Dex monk survived about a round longer.
That discussion, however, was limited to pure melee- it didn't account for differences in tactics (as outlined above) and assumed that all combatants had simultaneous initiative- thus ignoring the Dex monk's initiative advantage.
See also
http://www.enworld.org/forums/showthread.php?t=198272&page=1&pp=30 for a bunch more info on Monk builds.