The whole concept of gentrification is flawed. Poor, hard-working, noncriminal people are always going to find themselves living among less savory types in the cheap areas where people with more money don't want to live and city services are bad. Unconventional types are always going to take lower paying jobs, be more tolerant of poor people, and be willing to pay the price of living in unsavory areas. Unconventional types who grew up in more "middle-class" environments are always eventually going to start demanding better services and creating attractions. Less conventional types are always going to find unconventional types less boring than themselves, follow them to these areas, and demand even more cops, etc. Nothing about this changes the resources of the original, non-criminal poor people - who get displaced.
There are only two ways to change this - and no particular societal will to do either: more support for poor people so they don't have to live in "bad" areas and more options for unconventional types (artists' grants, etc.) so they don't have to move into the poor sections of town.