Yes, and of course economists do test their models empirically. But many economic models are inherently or practically untestable because the quantities they employ are inherently or practically unmeasurable. And even when you can measure most of what you need, models of complex economic phenomena just haven't worked. The lesson most economists took from the failure of efforts to build useful CGE [1] and DSGE [2] models in the 1960s–1980s was that this approach was a dead-end.
Agent-based models, though built on better-founded micro theory, are arguably even harder to get right because agents are adaptive in unexpected ways. And because it's possible to make many models give results that "look right" if you fiddle with the parameters enough, you're just not going to convince anyone that you've built a model that represents the way the world really works.
Nobody trusts a black box. I think that's why most economists still build little mathematical models that try to give some targeted insight into some small aspect of some economic phenomenon. If you can understand how a model works (and, again, you usually don't "understand" simulations—all the interesting stuff is emergent), you feel like you've learned something about how the real world might work. Then you can get down to bickering about assumptions, which effects dominate, etc.
1. http://en.wikipedia.org/wiki/Computable_general_equilibrium
2. http://en.wikipedia.org/wiki/Dynamic_stochastic_general_equi...