I also had the same question and shared the same concern.
The short answer to your question “what exactly is this VNET going to do as it is an orphanage.”
Is NOTHING
The detailed answer by @Ken W MSFT is detailed, valuable and perfect. And you already knew that.
Your security team is driven by the fact that Microsoft built-in policies, and Security baselines for Azure key vault and Azure Security benchmark all recommend that you never reach AKV from public internet and therefore reach it ONLY by private link or service endpoint as explained in details above but that all assumes that you have a VNET and VM IaaS which is NOT your case.
It does require someone who looks at a wider view and not follow the recommendations blindly without understanding what they mean.
I say that while I am open to be wrong and challenged but I have seen such dilemmas because I worked and lived in both worlds as Cloud Solution Architect and a Cloud Security Architect.
So, to meet your security requirements you can do one of the two options:
Change your PaaS application into IaaS, have a VM in a subnet in a
VNET and make the property configurations like explained above.
Promote the hosting plan to isolated, and integrate your App
Service with VNET and have the VNET Access the AKV other resources
as shown in this link
Here is the Guidance for the security that your security team is recommending. but it is way more costly than your solution.
Guidance: When using App Service in the Isolated pricing tier, also called an App Service Environment (ASE) you can deploy directly into a subnet within your Azure Virtual Network. Use network security groups to secure your Azure App Service Environment by blocking inbound and outbound traffic to resources in your virtual network, or to restrict access to apps in an App Service Environment.
By default, network security groups include an implicit deny rule at the lowest priority and requires you to add explicit allow rules. Add allow rules for your network security group based on a least privileged networking approach. The underlying virtual machines that are used to host the App Service Environment are not directly accessible because they are in a Microsoft-managed subscription.
Protect an App Service Environment by routing traffic through a Web Application Firewall (WAF) enabled Azure Application Gateway. Use service endpoints in conjunction with the Application Gateway to secure inbound publishing traffic to your app.