Because Deltachat has an e-mail backend, we already have key-lookup services; we have WKD. We choose not to use it by default because in-person scans are far easier for the average user to do securely.
You certainly do not need a mobile. Desktop-to-desktop communication can be set up via another secure communications channel; a printed QR invite code and a webcam would work, as would sending the link via another secure messenger.
See Advanced contact-adding tutorial for non-default ways to share contacts.
For really extensive design discussion of WKD and Deltachat, see The life-changing magic of WKD .