Why do IIS application pools need to be recycled?

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.

From https://weblogs.asp.net/owscott/why-is-the-iis-default-app-pool-recycle-set-to-1740-minutes

You may ask whether a fixed recycle is even needed. A daily recycle is just a band-aid to freshen IIS in case there is a slight memory leak or anything else that slowly creeps into the worker process. In theory you don’t need a daily recycle unless you have a known problem. I used to recommend that you turn it off completely if you don’t need it. However, I’m leaning more today towards setting it to recycle once per day at an off-peak time as a proactive measure.

My reason is that, first, your site should be able to survive a recycle without too much impact, so recycling daily shouldn’t be a concern. Secondly, I’ve found that even well behaving app pools can eventually have something sneak in over time that impacts the app pool. I’ve seen issues from traffic patterns that cause excessive caching or something odd in the application, and I’ve seen the very rare IIS bug (rare indeed!) that isn’t a problem if recycled daily. Is it a band-aid? Possibly, but if a daily recycle keeps a non-critical issue from bubbling to the top then I believe that it’s a good proactive measure to save a lot of troubleshooting effort on something that probably isn’t important to troubleshoot. However, if you think you have a real issue that is being suppressed by recycling then, by all means, turn off the auto-recycling so that you can track down and resolve your issue. There’s no black and white answer. Only you can make the best decision for your environment.

There's a lot more useful/interesting info for someone relatively unlearned in the IIS world (like me), I recommend you read it.