In his pre-ascension state, Mayor Wilkins is apparently invincible to Buffy, the Scoobies, or anyone else who crosses him. He attempted to have the volcanological research of Lester Worth squashed via Faith: he knows that in fully-ascended/Big Time Demon form he will be vulnerable to death, yet the acquisition of ultimate power is his main objective so invulnerability would definitely be an advantage. Why sacrifice these abilities in order to become a big combustible snake?
He was a soulless servant to demons of the Hellmouth and was seeking to become more powerful than them
Mayor Wilkins had committed himself one hundred years prior to the events of Buffy to what is termed the Ascension. This backstory is revealed in scripts for Buffy: The Animated Series. There, Wilkins was a human who originally arrived in California in the 19th Century, and founded Sunnydale on the site of Boca del Infierno shortly after a Vampire Slayer, Naayéé'neizgháni, had been killed there. Wilkins stumbled upon the Hellmouth and found it overrun with demons because of the death of the Slayer. He ended up making a pact to avoid being killed himself. He agreed to make Sunnydale a refuge for demons, free from outside interference, so that they could feed on the inhabitants unchecked. As part of the deal, he gave up his soul. In 1899, he began planning his 100-year Ascension into the form of a pure demon — this is what you see happening in Season 3 of Buffy.
So his choice was to remain a soulless human maintaining a feeding ground for demons, or ascend to become a powerful pure demon, not under the control of other lesser demons.
Finally, note that his invulnerability was never stated to be permanent, but rather a temporary power that kicks in for the 100 days leading up to the Ascension. So (a) he became invulnerable because he was on the way to Ascension (these are not independent things), and (b) the invulnerability was not a permanent transformation.