Good morning Webster.
I'm not sure why someone would recommend a one-to-one relationship of web servers to JVMs behind an F5...
I happen to run an environment similar to yours where WebSphere is front-ended by IIS web servers and a pair of F5 load balanaces.
In my configuration, I have numerous WebSphere installations spanning quite a few hosts. Each application in WebSphere uses a web site in IIS to route traffic to the application/ websphere cluster (I'm running ND.) Ahead of that is the F5 that hosts the VIP (virtual IP) that the DNS entry resolves to. The F5 then forwards the request to the IIS webserver defined in it's "Default Pool" (F5 terminology) and uses the values defined we defined for the the F5 "Persistence".
The web servers we run are IIS, as previously mentioned, but they are
shared. I perform a custom installation of the WebSphere PlugIn on IIS (I don't use the installers) to do what I want. It's essentially creating a new dedicated website in IIS, then isntalling a new isntance of the PlugIn to run for that website. I ultimately create the web site in IIS and then map my applications to include these resources and generate the plugin. I then push the plugin to the IIS website.
This approach lets me load balance (via F5) across a small cluster of IIS web servers (which are redundandt) and route traffic to the correct WebSphere instance. The benefits include web site redundancy, hardward loadbalancing via F5, individual websites and plugins, etc.
My configuration my be a bit different than what you aim for as session persistance is at the JVM for the applications I'm hosting.
Hopefully this proves useful!
Erik