Governments in democratic societies are elected to serve their citizens, not to impose some ideological view of what they would prefer society to look like. If they do try to pursue equality in wealth and income they will almost certainly reduce both. While there are some who would prefer a society that was more equal rather than one in which everyone became wealthier, this is unlikely to become a popular view. Becoming richer is something that matters much more to poor people than to rich people.
People are different and they have different goals in life. Some are born more talented, and some put in the effort and the time it takes for them to become so. Some people have more economic value than others, though this is not to say they have more moral worth. People will pay money to see a talented celebrity or sportsman perform, and those individuals can become richer in consequence. To equalize incomes is to prevent this happening. Since higher earnings make possible higher savings and greater wealth, to equalize wealth is to prevent people from accumulating the proceeds of their talents.
Most people would prefer society to make provision for the unfortunate or destitute, but this means ensuring they have a decent standard of living, not making them equal in wealth and income with richer people. Governments that strive for equality can only do so at the expense of liberty, by preventing the free choices and exchanges that people would otherwise make.
Egalitarians have tried to redefine poverty as a percentage of average income, but this is not what it is. Poverty does not mean inequality, it means not having enough resources to get by and to live a decent life. Many would rate opportunity above equality, thinking it more important that people should have the chance to develop their talents and abilities and to raise their standard of living. Many would prefer governments to help make this possible, rather than attempting to equalize wealth and income.