Section 15.15 from Bruice, Friedel-Craft Alkylation of Benzene

Hi folks,

I had a quick question about the Friedel-Craft alkylation of benzene mechanism that's shown on pages 645/646 of the textbook.  Where it says "Generation of the electrophile," we see that an alkyl chloride becomes a carbocation intermediate when the Cl atom leaves and binds to the AlCl3.  My question is, why does this work for primary alkyl halides, since the chlorine atom seems to leave in an almost SN1 fashion?  Wouldn't the carbocation formed be too unstable?  Also, by looking at the mechanism, it doesn't show anything displacing the Cl, or pulling it off the alkyl halide.  Would this reaction work for methyl-chloride (which would form a methyl cation)?  Just curious, the process seems to form a really unstable intermediate in some cases.