I thought so too, but I felt the urge to get back into SLR photography recently so I picked up an old Nikon D3 on eBay and the difference between it and my iPhone SE is like night and day. No matter how you tweak them small-sensor photos just look flat and drab in comparison, or garishly oversaturated.
Both flat/drab and garishly overcolored pictures can be easily fixed in Photoshop, except when noise or lack of dynamic range gets in the way (i.e. the detail never gets captured, or one or more color channels get clipped).
The problems with phone cameras (and small sensor cameras more generally) are (1) hitting the resolution limits of the optics, (2) noise, (3) lack of dynamic range, (4) lack of choices in quality lenses, (4) fixed aperture, which means no creative focus effects, and poor performance in low-light settings, (5) software based (and therefore slow and sometimes inaccurate) manual controls over shutter speed, focus, flash, etc., (and more generally, a much less efficient or adaptable physical user interface than a dedicated camera) (6) often limiting output formats, with lots of in-camera processing wiping out data from the raw image.
Any 6+ megapixel DSLR (e.g. the ones from the early 2000s) with a nice lens easily outclasses the iPhone or any other phone camera, in the hands of a photographer with basic competence.
On the other hand, phone cameras are amazing for their ridiculously tiny size, and their cost is obscenely low after the economies of scale kick in. They take much better pictures on average than the <$50 35mm film cameras from the 1990s, especially when the photographer is a complete beginner (those are the cameras I think of as their spiritual ancestors).
Oh yeah; I remember too realizing that I didn't need my A4 scanner anymore, a phone cam picture was good enough to email a readable document! They're impressive no doubt but SLR technology hasn't stood still either.
