To paraphrase Blue Dog, an attending over in the FM forums, if you think you could be replaced by a midlevel, then maybe you should be. Quality physicians have very little to worry about.
Are things changing? Of course. Let your own skills (and those to be) speak for themselves. All it takes is a missed zebra by an autonomous midlevel for patients to realize that they are safer overall in the hands of competent physicians. Say the numbers of DNPs practicing autonomously skyrocket. Odds are misdiagnoses will also be on the increase and these statistics will find their way into studies, media, etc. Folks will run for the hills to find physicians.
All of this said, the average DNP does not see her/himself as being the equivalent of a MD/DO and only wishes to serve his/her role on a healthcare team, which IS the future of the practice of medicine. Those wishing to fly-solo, well they have their work cut out for them. Just wait until it starts raining lawsuits and Noctor Smith finds herself chin deep in malpractice insurance. Lawyers will have a field day with this $hit and I'm sure those in the know, standing on the sidelines, are just licking their chops waiting to pounce on easy prey.
Tl;dr version: nothing to fear. Control what you have control over- becoming a kick ass physician.