The role of an enterprise architect is to work with stakeholders, gather requirements, create time lines and then hand their work over to another team to implement and continue to provide governance. At best you might be lucky to get access to some sort of test environment. I am TOGAF certified and like you before I started didn't understand what it was before I started. The trainer I had described it as creating cartoons for executives. I still got the cert but realized it really wasn't for me. I will say that I think the role is very important and as an implementor is designed to answer the questions I often have when building something like number of users, availability requirements etc.