Agree that you need to get a pretty high quality P&S to be much better than the top end phones these days. There is a camera space between top end phones and DSLRs, but even the least bulky of them are considerably more bulky than a phone. And if a digital screen is your end viewing option, then there is no quality benefit to a P&S, but many drawbacks. The biggest other advantage is probably that you can get a zoom lens, if you are the sort of heathen who likes such things.
That said, if you want a serious camera for prints but a DSLR is too bulky there are a few good options. I recently got a Fuji X70 for travel. It is just small enough to carry around when I am actively wanting to take pictures, but I would never take it with me on just a day out. But it is a lovely camera built for old school camera types who want the ability to easily closely control the technical aspects of photography. The best feature of it is that it has a flip out screen that essentially emulates a medium format waist level finder of old. That's how I learned to really take pictures, so I really like it.
If you want a zoom lens, the Canon G9x is pretty cool, as is the Sony RX100 series. Here are some options:
https://www.dpreview.com/reviews/2017-roundup-compact-enthusiast-zoom-cameras
https://www.dpreview.com/reviews/2017-roundup-consumer-long-zoom-compacts
https://www.dpreview.com/reviews/2017-roundup-fixed-prime-lens-cameras