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He figured that having Angelus around would mean no Angel, basically, and that was good.
Taking care of Buffy was a bonus but you'll notice that the Mayor merely asked 'Angelus' what he wanted to do, and Angelus came up with suggestions all on his own. The Mayor was happy enough that he would keep the (good) slayer off of his back.
I mean, The Mayor is invulnerable and is gonna become a big demon-y thing, I doubt he's worried about what Anglues might do to him.
Wilkins had vampires on his team already, but they didn't seem to be all that bright. Maybe he wanted to recruit Angelus to lead them. Then again, maybe he was just getting him as a gift for Faith. Either way, even if they had successfully de-souled Angel, it would have been a mistake. Angelus doenn't work well as a minion. He would have been far more likely to turn on Wilkins and either kill Faith or force her to kill him.
I don't think it was elaborate. Take away Buffy's strongest ally, together with Faith they kill Buffy. He is used to generally subservient Vampires so he probably did not understand that Angelus might be more likely to screw up his plans than Angel. At minimum he betrays and kills Faith once Buffy is subdued/dead.
It sort of reminds me of 'The Dark Knight' where the mob hired the Joker to kill Batman. They had no idea what they were unleashing on the city.
He wanted Faith to give Angel the one moment of happiness but Angel was not willing. With Angelus around, Buffy would be busy and could not stop the ascension. His plan with Faith was as shown in "Enemies":
There's no need to convince me. I'm
sure you gave it your level best. I just
don't understand what that boy could
Try Buffy Summers. Like in the big fat
Don't be discouraged. You're a bright,
young, energetic girl with a whole life
ahead of her and I won't tolerate
brooding. So you couldn't give him
one moment of true happiness.
I was thinking more along the lines of a
long weekend, but okay.
And he spurned your advances. So be
it. There's more than one way to skin a
cat, and I happen to know that's
factually true. We want to take Angel's
If you can't do it by giving him
happiness... well by golly, we'll
just have to do it in the most
painful way imaginable.
Angelus is pretty much a Prince of Vampires. The Master deemed as the creature he wanted at his right hand, he was a member of the Order of Aurelius he took over Spike's gang in a few minutes, all other vampires seem to both fear and respect him. Heck, even the Beast, who in demonic stature far outranks a lowly vampire, was willing to entreat with him. So, if part of your plan requires a lot of Vampires, you want the best on your side, and to choose Angelus as one of your fell paladins is a no brainer. Consider how Graduation would have gone with Angelus and Faith present.