It's a title for a degree, not a job description.
Anyone who puts in the work to earn a doctorate degree deserves to use the title doctor. Yes, I call my physician "doctor." I also call my dentist "doctor" and my college professors were addressed as "doctor." Psychologists, school superintendents, reverends, anyone who holds a doctorate in any subject is addressed as doctor. Why should a hard-working, advanced-practice nurse not be afforded this honor? No one is suggesting that nurses tack MD to the end of their name. I don't think it's misleading if someone's nametag reads Dr. Jane Doe, DNP. If a patient asks what the DNP or DNAP stands for, then tell them. It's a wonderful opportunity to educate the public.