As an Asset Library Administrator/Owner you can't access Asset Libraries (neither through the Control Panel nor through the Site Administration Panel).
Environment
DXP 7.3
DXP 7.4
Resolution
This can be achieved by creating a Regular Role with some specific permissions and then assigning it to the Asset Library administrator.
Steps:
Add new Regular Role: "AL Admin"
Permissions:
Create/Edit your user
Add membership to your Asset Library
Assign roles to the desired user:
Regular role: "AL Admin"
Asset Library Role: "Asset Library Administrator" (select the preferred one)
Additional Information
LPS-118200: Asset Library Administrator can't access his or her Asset Library