A group of Microsoft Products and technologies used for sharing and managing content, knowledge, and applications.
Hi Mirek,
Thank you for posting in the community forum here. I can understand your willing to make the “people with existing access” link as the default link. If so, people can copy and paste the item link to others easily without granting new permissions. And the people who are having existing permissions can click the link to go to the item easily.
To address your concern, here’s the UserVoice: Add "People with Existing Access" to the Default Link Types under SharePoint Admin Center's sharing options. We suggest you vote and monitor it. The higher votes may let the product team pay more attention to this. And this is the best way to let us hear your voice and to make our products and services better for you and others.
Thanks for your understanding,
Rena