How Azure Monitor's Implementation of Private Link Differs from Other Services

Very detailed article. Actually came across this because I have a customer who is having the issue where because they have a private zone configured for privatelink.monitor.azure.com for their AMPLS, the logs blade for their log analytics workspaces all don’t work. This is because currently, the logs blade appears to rely on “breeze.aimon.applicationinsights.io” which includes a privatelink.monitor.azure.com CNAME record in the chain. And since all DNS  queries under privatelink.monitor.azure.com are conditionally forwarded to their DNS appliance in Azure to ultimately be forwarded to the proper Azure DNS resolver, and there is no a record in that private DNS zone for breeze.aimon, the logs blade never loads for them. What’s the Microsoft recommended solution here? Is there one that doesn’t involve enabling public DNS fallback?