The web keeps throwing exception other than log the errors. A small error/exception can crash the whole web page. Instead of letting the small errors/exception crash the web page, we prefer to show part of the web page. The exceptions in web page show to our users but it's hard for us(engineer) to know the exact logs. Logging can help us debug.
In conclusion, it may be better for us to log the exceptions and errors instead of throw them on the web UI.