Unfortunately for the Cardiff-based quango, even fewer people, at least of the right calibre, seem to like the idea of being in charge of it.
A statement by ELWa said there had been a "rigorous" selection process.
Being a Welsh-speaker was "desirable but not essential," according to a spokesman. In fact, the selection process was so vigorous that none of the shortlisted applicants was considered good enough by ELWa's national council.
But don't panic. Council chair Sheila Drury, explained that the inability to hire anyone merely reflects the importance the organisation places on the high-profile job. She said: "Given the challenges facing the organisation, and the need to maintain the progress that has been made to develop its executive strength, it is especially important that there be the closest possible match between the appointee's capabilities and the advertised requirements of the post." Quite so.