I am afraid we can't really change it. It's been at 06:25am (UTC in our case) forever and people expect that. Changing it would break the current expectations of people. Note that this is true for all services and software and it hasn't really caused an issue for a long time. So we should make a better job of surfacing and fixing the issues, not changing the logrotate schedule
In general I agree with your note but I was thinking of preventing similar down times in several levels. I'm already working on binding the services and the config files but this seemed like a good idea to me. I leave it to SREs to decide, feel free to close this task if you still think it should not happen.