I used the example of big prints (big here means bigger than A4) because it's the most immediate demanding application that I could mention. With a phone you also don't have the resolution to spare to apply perspective correction to photos of buildings, dynamic range to deal with less than gentle, bright scenes, etc.
I have a 3 year old print on my wall of my kids, taken with an iPhone 5, cropped from a horizontal framing to vertical, and then printed at 11x14". I did a bit of post-processing on it to sharpen it up, and it looks fantastic (until you look at it from less than a foot away). I need to repeat the process with the X's camera. ;)
Modern kit lenses are optical marvels. A couple of decades ago you couldn't buy a lens with the quality and versatility of Nikon's 18-55mm kit lens.
Leica M rangefinders still have the best controls for non-action photos, which is a bit sad for a design from the early fifties.
That's probably the basis for my impression. I basically only use auto and am not educated enough in photography to use manual mode in most cases.
Increasingly I'm happy enough with a phone (giggle pixel 1 which has a halfway decent camera + software support) for walkabout use, but the benefits of a small DSLRs for holidays or other special events is hard to beat.
But who is actually making big prints? I've never done a singe one and likely won't do anything bigger than a photobook page. That's exactly my point about dslr's becoming redundant for more and more users.
I own a 500€ low end dslr and it feels worse than my 500€ phone that I carry with me anyway.