Even inadmissible heuristics can have their place, and it is easy to reason about how suboptimal they can be: you might want to trade off optimal results for performance (i.e. ignoring some part of the search space that should be searched) or to make an agent in a game a little stupid or stylized (e.g. prone to zig-zagging).
It is complete and optimal, with provable properties.
Whenever there exists an admissible heuristic, you should use A* over Dijkstra's algorithm.