we have this problem with Web Key Service which is our idea to publish keys automatically in a Web Key Directory. Kleopatra has no support to search in Web Key Directory (because GnuPG only allows you to import directly through --locate-key / --locate-external-key and this does not really match kleopatras "Search" interface. But this is probably a different issue.
What I would very much like to have would be both a WKD / WKS status indication and the option to publish a key in a WKD through WKS in the Certificate Details of Kleopatra.
I'm currently not recommending WKD / WKS to our gpgcom customers because the support is still too lacking in my opinion.
Kleopatra currenlty interacts with WKD if you enter a e-mail address in file encryption then it will do a --locate-key and find / import a key from WKD.
KMail has some support for WKS through the Accountwizard so genral handling of mails is already there.
Kleopatra could add some interaction with the QGpgME WKSPublishjob and basically then try to call the MUA to mail the WKS request. When we test that with KMail and GpgOL we are already cover a lot of Kleopatra users.