What you miss here is that you assume Sharon and Arafat are on equal footing, with comparable resources at the disposal. You would (rightly) assume Mexico and the US would be so positioned in the scenario you outline.
I'm not convinced Arafat has the polictical will of his people (more likely he has a price on his head not unlike the President of Pakistan or Saudi leadership) or the resources (made worse in light of IDF's obliteration of several Palestinian police facilities) to meet Israel's demands.
Seems like Israel's not too interested in Arafat's own problams and, not surprisingly, he's not too interested in meeting their demands.
Furthermore, your point was the arguement sucessfully presented by Arafat at Oslo in 1993. Israel conceded to allow him a police force of 20,000 armed with automatic weapons. They stood by and allowed this to double despite being limited by contract. It is incumbent upon Arafat to use these resources in the effort of peace, not war.
It doesn't help to see the police that were supposed to be used to help enforce the peace involved in the terror. For example, if you recall the few weeks before the Intifada broke loose (before Sharon visited the temple mount) a Palestinian police officer shot and killed his Israeli partner while on joint patrol. This is the kind of stuff that makes trust break down. And it spirals into an abyss if it is not brought to an immediate halt. I don't believe Arafat has done nearly enough to wind down the violence. He should have outlawed Hamas after the first bombing of the disco. Instead, they have continued to operate inside his territory to this day.
If Arafat is incapable of shutting them down, he should negotiate for more power, or stand back and let Israel do it for him. He can't just stand there doing nothing.