I would actually argue that integration does not really mean the same thing when we are talking about "the black ghetto" and "fresh off the boat" immigrants. Both are minority populations, but the similarities really end there. Integration in the classical sense of the word works absolutely great for the "fresh off the boat" immigrants, with the notable exception of Latin American populations. In certain places in the country, it's very common to have neighborhoods that speak almost exclusively Spanish. Obviously, the closer you are to the Mexican border or to places of refuge for Cubans in Florida, the more likely you will see that. Ignoring that exception, generally, integrating those people into the community, getting their kids into English-speaking schools, etc. effectively does the trick. In that sense, gentrification can totally work.
When speaking to the "black ghettos," what you are really talking about is an established American subculture that exists independently of the larger American culture. In that sense, the word gentrification is really talking about trying to absorb those people into the larger American culture, or, as some might view, swallow that culture up. Whether or not it should happen is a separate debate. So in that sense, gentrification doesn't work because it's trying to address two problems with the same approach. What you would need to do is alter the subculture to make it more compatible with the larger culture, or you would need to persuade people from that subculture to abandon it in exchange for being a part of the larger culture. In that sense, gentrification doesn't really work because you're just redrawing boundaries without really addressing cultural differences or values.