Websites are intended to keep running (albeit in a stateless nature). There are a myriad of reasons why app pool recycling can be beneficial to the hosting platform to ensure both the website and the server run at optimum. These include (but not limited to) dynamically compiled assemblies remaining in the appdomain, use of session caching (with no guarantee of cleanup), other websites running amok and resources getting consumed over time etc. An app pool can typically serve more than one website, so app pool recycling can be beneficial to ensure everything runs smoothly.
Besides the initial boot when the app fires up again, the effect should be minimal. Http.sys holds onto requests while a new worker process is started so no requests should be dropped.