@WASA-SCHRADER Christian - Welcome to Microsoft Q&A and thanks for reaching out to us.
Reiterating the answer here for a broader audience. You should be able to on-board Linux machines with the single server onboarding script and no service principle. But if you would like to share the feedback to the product team as the script is skipping the onboarding part, please share it here: https://feedback.azure.com/d365communityHope this helps. and please feel free to reach out if you have any further questions.
Please don't forget to "Accept as Answer" and click "Yes" if the above response is helpful, so it can be beneficial to the community.