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I enable the secret question pretty soon (probably during the account creation procedure), and later came to read that resorting to its use would indeed lock your account, being the unlocking procedure not immediate nor trivial. As such, I left the secret Q/A there, on the profiles, but often felt like I really wanted to delete it (having a signed message on the appropriate thread seemed more fitting). It took me ages to delete it, but it’s really rather trivial:
<...> I had this step (deleting my secret question) pending for ages, and it has not been until now that I’ve gone ahead with it. Just a minor observation: Since the Answer is displayed as blank, you can’t really delete the content of the field. I therefore deleted the question, assumed that the answer deletion would be deleted, and hoped for the best. Logging out and back in again works fine, so I figure that was all that was required (+ > Enter your "Current Password" > Click "Change profile" button <…> as you stated).