You can "delete" things in an append-only ledger, in the sense that you can update the state with e.g. a tombstone marker.
On a higher level you can't delete things anyways, because as soon as you has shared them with a third party the control is out of your hands anyways. Just because current social networks try to hold up that facade doesn't make it a reality.
Sure you could make tombstoning past messages and making their contents inaccessible a more central feature, but there is nothing inherently wrong with append-only social networks.