I've been asked by Azure support to open the question here, though i think this is an AKS bug.
When deploying a cluster each node 'node.status.addresses' should show an externalip or hostname of the node by design but there is a VM name in hostname address in instead of it in AKS made cluster. Which makes it is really hard to know node public ips for various reasons we need them.
Is there any standard or nonstandard way to get node public ip ?
There is the public IP exposed for the Azure Kubernetes Service, but it's not directly to the node. Actually, the Kubernetes node will not be exposed to the internet with a public IP.
The AKS nodes create in a VNet on Azure and access or can be accessed through the Azure Load Balancer with a public IP. The VNet is a private network as a resource of Azure. For the VNet, there are two types such as Basic and Advanced. You can get more details, see Network concepts for applications in Azure Kubernetes Service (AKS).