Your experience of high-quality care in NYC mirrors mine here in the N.C. Research Triangle area, with excellent med schools and teaching hospitals at both Duke U. and UNC Chapel Hill. And a rich density of excellent PCPs and specialists in the area.
My mother's PCP, notwithstanding that stupid slip -- occasioned, as you so rightly say, by our pathologically over-connected culture -- is possibly the best she has ever had. Very attentive, inquisitive, responsive, readily referring to specialists, even -- especially -- when 'It may be nothing serious, but we need the specialist to look into it and be sure.'
A 180deg change from the '80s and before, when Check 'em in and shove 'em out the door ASAP was the modus operandi of most general practitioners. Living in Boston in the '90s and the oughts, and being friends with a number of doctors, medical department directors, and faculty at the teaching hospitals, I watched with great satisfaction and relief the self-aware, well directed change toward patient-centered medicine.
Although at the same time, as you (and I above) observe, the patient, and the patient's closest support people, still have to be the lead advocate for the patient's interest.