But we need to distinguish the right to transparency from the right to vote.
There have been calls for the post to be directly elected - some Eurosceptic condemnation of the Lisbon Treaty was based on the fear that it created an unelected executive President of the EU, rather than the occasional chairman/woman role that it will actually be. If the office had really been an executive post, then the outrage at the lack of direct elections would have been understandable - after all, the electoral college that elects the President is made up of the governments of the member states, and though they have legitimacy as directly or indirectly elected bodies themselves, having an executive post elected by a twice-removed indirect method would have been too much. But then that's the point - it's not an executive President.
So, no, you shouldn't have a vote on who gets the job. Just as the President of the European Parliament shouldn't be directly elected (MEPs elect the post), so it is justified that the European Council elects its chairman. Direct elections for such an office would be pointless - why focus on making what is essentially the "Speaker of the Upper House", who doesn't even have a vote, directly electable, when increasing the accountability of the Commission and participation through the European Parliament are the real, substantive challenges?
That's not to say there are problems with the selection process; ideally the candidates would apply for the post, and be subject to an open and transparent debate in the European Council and/or an open interview before the European Council. Though there may be some diplomatic hang-ups about this level of openness in what is an intergovernmental institution (note that this means you can't always apply the same rationales to it as you can to the supranational institutions!), I don't think the argument that the selection process should be secretive and elitist can be justified:
"The bottom line is surely this: if the EU sees any merit in having big, serving figures given these big new jobs, then opacity is the price to pay."
This assumes that former and current government leaders form the only qualified group that you can draw on to fill the post, so you mustn't scare them off by opening the process so much that candidates risk losing face by not getting picked. While it's true that openness and transparency isn't likely to excite Europeans into caring about European politics (I don't see the performance of Barroso during Commission President's Question Hour being poured over each month on the news, do you?), and direct elections aren't likely to do better (after the novelty value wears off, and people realise that the post isn't executive, do you think that its election will even manage the turnout of the EP elections?), arguing that opagueness is "good" is just ridiculous. There may not be a cause to directly elect the President, but open discussion and debate of the roles and politics of the candidates and the institution itself has its own value.
We should be concerned about holding the European Council to the principle of transparency, not arguing for the vote when there's no firm ground for doing so.