Dems generally see poverty and inequality as a useful political tool: here's how and why...

First, because they're not talking about poverty much anymore-- and poverty is the more important concern. Why the near-silence on poverty? Well, it has proven intractable-- at least by the government's primary statistic for measuring it. Their favored ways to try to address it have obviously failed. For those who think thru the cause/effect, the "solutions" have obviously caused a ton of trouble-- in particular, by subsidizing the obvious troubles with family structure and stability. 

Second, we know that Dems aren't all that interested in poverty, given their policy preferences. In sum, they actively harm the poor (especially African-Americans) from cradle to grave. They support all sorts of redistribution from the poor/middle-class to the wealthy: farm policy, subsidies for college, bowing to crony capitalism in K-12, and so on. (Real liberals still talk about crony capitalism a lot, but unfortunately, there are so few of them!) They tend to see the problems of poor as external to them-- a debatable position-- but they ignore many of the external causes that they foist about the poor! But here's a punchline if you need one: How often do you hear Dems complain about the 15.3% tax on every dollar earned by the working poor and middle class?

As for inequality, Democrats are unaware of or ignore the profound difficulties in measuring income inequality and the even-larger problems with wealth inequality-- overlooking these problems to use the topic as a convenient political tool. My favorite in this realm: income inequality is mostly unchanged when you look at individuals, but has increased dramatically between households-- indicating that the massive changes in household structure over the past few decades are the key to understanding the issue. Obfuscation on this issue indicates a key point of ignorance or a disappointing point of demagoguery.