As a relatively new abstraction, matroids clearly enjoy a rich theory unto themselves and also offer a viewpoint that suggests interesting analogies and clarifies aspects of the foundations of venerable subjects.
All that said, a very harsh metric by which to judge such an abstraction might ask what important results in other areas reasonably seem to depend in an essential way upon insights first gleaned from the pursuit of the pure theory. So I'd like to know, please, what specific results a matroid theory partisan would likely cite as the best demonstrations of the power of matroid theory within the larger arena of mathematics.
(I realize that mathematicians in one field will sometimes absorb ideas from another field, then translate back to their preferred language possibly obscuring the debt. So important papers that somehow could not exist without matroid theory should count here even if they never explicitly mention matroids.)