Alex Cullen of Forrester poses the question and provides the usual expert answer which can be paraphrased as "it depends".
The neat accounting view that there is an ongoing programme of delivery from which subventions can be drawn to pay for necessary evils of CIO, strategic planning in a manner similar to large plant replacement misses the point that you would not need active enterprise architecture people if everything was planned out.Rather than comparing EA with IT management overheads like the CIO office, "research and development" within the wider enterprise may bear more fruit. In non-productive organisations like government agencies, policy development would be equivalent to R&D. Then the thinking around EA funding would be closely aligned to the enterprise strategy rather than the current IT problem set. Of course, if you don't do R&D in some way then there is a pretty clear message that you are not interested in strategies so why do EA?
Practically though, if you believe that EA has a benefit for the organisation, you get the money from wherever is feeling the most pain from the lack of whatever EA will deliver.