Hello,
Thank you for posting in Q&A forum.
There's no need to install LAPS on all DCs.
LAPS CAN automatically manages and backs up the password of a local administrator account on your Microsoft Entra joined or AD-joined devices. The password will be saved in AD storage and synced to other DCs as well, hence there's no need to install LAPS on all DCs.
For further details, please refer to Microsoft Official Documentation: https://learn.microsoft.com/en-us/windows-server/identity/laps/laps-overview
Hope this answer can help you well.
Best regards,
Jill Zhou