When publishing an ASP.Net Core website project in Visual Studio, under "Site Extensions Options" I am offered this option:
What does selecting that option do? My project already includes the Microsoft.ApplicationInsights.AspNetCore
NuGet package, and logging via the Microsoft.Extensions.Logging.Ilogger
extension method works as expected to send logging information to Application Insights.
So, that Install ASP.NET Core Logging thing in Visual Studio is all about making your life easier, when you're using Azure Application Insights for logging in to your ASP.NET Core web app. It helps set up something called the Application Insights Profiler during the publishing process. This Profiler gives you extra details about your app's performance and issues when it's running in Azure. It just helps you get more out of Application Insights.
To answer simply if your logging is already good and you're not looking for super detailed profiling, you might not need to bother with it, but it's handy for some extra troubleshooting if you want you can enable it.