I would like to share an idea about an option for setting Session Timeout value in Servicecenter, it will be easier to manage this value from Servicecenter.
I would like this too, but it means that the Web server would need to have the ability to write to its own configuration files, which I would consider to be a security hazard.
There is an extension that does exactly this from your application. Just look for the BrowserSession extension in the Forge.
This means that for all applications you could set this in a site property or you create a generic function to fetch the timeout from a central location.