TOGAF describes Enterprise Architecture as a process, something to do. It optimizes the legacy of processes into an integrated environment, to support the delivery of the business strategy. It then recommends how to practice enterprise architecture, using the TOGAF framework.
There are many other definitions exist, each in increasing complexity and vagueness. Almost all of these definitions tell you what to do and how.
In the book Enterprise Architecture As A Strategy, the authors define it as a thought process.
Our use of the term refers to the high-level logic for business processes and IT capabilities. IT unit will develop far more detailed architectures of applications, data and technology. Some companies refer to these architectures as the enterprise architecture can be confusing. (paraphrased)
Further they go on to discuss four stages of Enterprise Architecture maturity. Interestingly, these stages are characterized by the ratio of enterprise and local systems. Even in the most mature stage, the local applications are present, with a decent share.
So, the goal of an enterprise architect is multi-fold.
First, to organize the logic for business processes and technology capabilities. Second, to arrive at an optimal distribution of technology capabilities across different systems. This is where I find the economic aspect compelling. Enterprise Architects maintain a balanced set of technology capabilities to fulfill business needs. Balance between manual and automated processes, local and enterprise systems, legacy and modern technologies.
Often, the practice of Enterprise Architecture is compared to town planning. While I disagree with this analogy in the context of software development, there is some merit from an economic perspective. Economics is one key aspect of urban planning, along with social, environmental aspects. The third goal should be how to shape the economic, social and environmental aspects of business and technology landscape. This expands the scope of enterprise architecture to look at developer productivity. This helps enterprise architects to define an evolutionary roadmap.
We need enterprise architecture to be more than just following a framework. And pursuing the economic, not financial, aspects of the business and technology landscape makes enterprise architecture a planning and thought process.