As I understand, this is a fairly popular approach. Direct solvers are usually more efficient than iterative solvers for < 100,000 unknowns, so you partition the problem into subproblems of roughly this size, use direct solvers on each subproblem, and combine them globally with some method like alternating Schwarz. It's also common use the domain decomposition method as a preconditioner for a global CG/GMRES solve.
You're correct that domain decomposition methods don't get the right answer in a single iteration. The alternating Schwarz method can be thought of as overlapping block Jacobi, just with very big blocks. The simple Jacobi iteration converges for strongly diagonally-dominant matrices; it's a similar argument to show that the alternating Schwarz method is convergent (for certain nice systems).
There are of course many variations on a theme. If you can make the subdomains structured grids, you might be able to use geometric multigrid on the subproblems rather than a direct solver.
Also worth noting is that some folks think of multigrid and domain decomposition methods as the endpoints of a continuum of algebraic multi-level methods.
If you're interested in these sorts of things, I highly recommend this book.