Calatrava is an unusual figure - he sits out and to one side of the bridge design profession to a great extent, while also being its contemporary exemplar. As far as I understand it, his firm now generally only produces the conceptual design of his structures, with the detail generally left to others to develop (see for example a PDF article on the Sundial Bridge). In this respect, they're more like architects than engineers, and it's possible to think of them as a franchise operation, passing out licenses in different communities to create and run their own piece of the Calatrava brand. He rarely, if ever, gets involved in engineering research, or publishing papers about his designs, unlike most of the great bridge engineers (e.g. Jörg Schlaich or Fritz Leonhardt). Calatrava gives the impression of being completely uninterested in the bridge design world outside his own office.
The Calatrava bridges around the world are brilliant in their design, engineering and marketing - and have earned their popularity. About 40 of them have been built so far all over the globe, so in a certain way they are the McDonalds of bridges. They all have the same processed and globalized esthetic, easy to digest but whose nutritional value is suspect.
Calatrava bridges are in their own way the Maccabi Tel Aviv basketball team of their branch. They trample all the competition, and wherever they spread their wings, there is no room underneath for other worthy bridges to sprout.
At the same time, his bridges are seen by many laypeople as the archetypal contemporary bridge design. Amongst professionals, it's easy to recognise a Calatrava design, as well as the numerous tribute structures. So predominant has been the post-Calatravan trend towards cable-supported gymnastics, that there is now often a very clear reaction against it (see for example RIBA's Bootle competition winner and New Islington competition runner-up).
Like McDonalds, Calatrava bridges may seem ubiquitous (especially so because of the number of similar tribute structures), and their consistent visual styling - tall; a cat's-cradle of cables; and puritan white in colour - creates a very effective brand image that promoters often want to buy into. In this respect, his bridges are more of an upmarket brand and in no way like McDonalds - think more of an expensive fashion label, perhaps.
Calatrava's bridges are also sufficiently neutral in all ways to achieve global success. They pay little attention to context or history; it's hard to imagine Calatrava designing a bridge that pays tribute to local heritage, for example.
For other bridge designers Calatrava poses a question: do you want the fame that comes from establishing a brand identity; or are you happy to be known only amongst your colleagues but retain integrity by respecting each site individually? It has to be said that most modern bridge masterpieces are by designers who follow the latter approach (e.g. Jürg Conzett). But I'm far from sure that makes Calatrava's method a bad thing. Whatever their merits in terms of cost (always too expensive) and their clear tendency to repeat and tweak a common theme, many of his bridges are hugely popular, and undoubtedly successful as sculptures. Is that enough, sometimes?