Seems that the problem you are talking about is the way the system automatically responds to flags when there is not moderator presence to review those and they are just left unresolved? Thousands of members may be too many for this community where you are experiencing this.
Would a solution to this be a change in settings so that there isn’t an automatic response to community flag reports, but those just go to alert a moderator who can make a decision about those? If the mods/admins at the site you are talking about aren’t open to new ideas like that then there may be nothing you can do.