Integrated amps have changed a lot in the last ten years, they have gotten a lot better. The $10K range is the real sweet spot in them. I have recently auditioned the Pass Int-60 (?), Luxman 509, and Audio Research I-50. $10K, $10K, $6K. They all sound quite good for their price.
To me… if you are building an audiophile system (which means you can never afford to buy what you want.. then they are not an option. You want to be able to upgrade a single component at a time… and an integrated is not going be as good as separates… OK, maybe not never because a two chassis solution will sound better because of greater isolation, but will cost more because of redundant parts. So, it can be real difficult theoretical trade off.
So, taken together, this all says, it depends. What is the house sound you like? You would choose the Luxman, Pass, or Audio Research based on their sound. The Audio Research just took me away, into the music, the Pass made my foot tap and really get into the music… the Luxman left me appreciate looking at the pretty knobs but not listening to the sound.
For the money, integrates can sound great, but not a good choice if you plan a better system.