In my opinion Sting will be remembered as one of the 20th century's most versatile songwriters. He has written classics in punk/reggae, pop, jazz and folk styles while never being a paid-up member, so to speak, of any of those categories. His lyrics can be simple, poetic, hard-hitting, insightful, but always to the point. And he's written some great hooks.
My favourite song from his Police era, So Lonely, contains all the guts and passion of punk, but adds lyrical dexterity........

"In the desert that I call my soul / I always play the starring role / So lonely, so lonely, so lonely"..

... and Fields Of Gold from 1993 seems to capture something of every folk lament I've ever heard in one haunting melody.
Probably his most famous song, 1983's Every Breath You Take, does very little for me, and Sting himself has admitted being surprised by it's mammoth success, especially with loving couples, who often seem to miss it's sinister undercurrent.

Some jazz aficionados have expressed resentment at his intrusion into "their" style; punk purists dislike his "dilution" of their angry music, and diehard folkies don't much like his modern "pseudo-folk".
But styles go in and out of fashion - quality lasts forever.