Good review. I think you might be too hard on the back half of "Regatta," which I would rank as one of their very best album sides - "On Any Other Day" is a throw-away track. The rest of it is really strong, touches on a lot of different styles, and has all the elements that made them a great band (unexpected rhythms, great vocal takes, arrangements with a lot of space, great textural guitars).
I agree that their first album is probably their best, but every record has a few gems. They went from energetic guitar-based, 3-piece rock songs recorded on a tiny budget.... all the way to massive-budget, complex arrangements with jazz elements and wide-ranging instrumentation (synths, keys, etc). "Truth Hits Everybody" is a million sonic miles from "King of Pain," but I think they're both brilliant.
To me, even those last two records were pretty cool, and as a band, they never jumped the shark the same way that Sting's solo records did (too self absorbed, self-important, and dissonant jazz wankery just for the sake of being weird). Summers and Copeland don't have the songwriting chops or the voice (obviously) like Sting, but Sting definitely needed them to save him from himself.