To understand why macroeconomists use DSGE as a tool, in general, it's a good idea to read up on the Lucas critique.
More colloquially, DSGE models provide macroeconomists with a laboratory that allows quantitative comparison (and ranking) of different economic policies. Further, the process of writing a model disciplines thinking: if one cannot write down a minimally specified model that replicates (to varying degrees of success) some real world dynamics of interest, then do we really understand what is happening to begin with? It's easy to play a casual story telling game that explains economic phenomena (with critical errors). We unfortunately see this all the time in politics, or even on CNBC.
Also, DSGE models do not all share the same objective. There are some medium and large scale models employed at central banks that are used to guide monetary policy. Other models are much smaller and stylized, and seek to answer questions about how a government should optimally finance itself, or how to tax different factors of production, or how informational frictions affect prices.
Finally, to answer your question on the state of dynamic general equilibrium theory, researchers continue to apply this mode of analysis to deepen our understanding of economic dynamics. This entails writing models of economic agents incentivized by objective functions, facing resource and informational constraints, interacting with one another and nature.
Every DSGE model has some fatal flaw which cripples it from perfectly explaining real world dynamics. Perfection is not the point of DSGE models, so when macroeconomists say that DSGE models are "useful" or "good", it's important to ask questions about the context of those descriptive terms. It's also important to remember that macroeconomists are, at the same time, some of the harshest critics of DSGE models.