Keeping a website online is hard. For smaller companies it is practically impossible. The largest companies with dedicated teams of engineers working on it still struggle. Automated reliability is important, but for many companies it’s more worthwhile acting on their alert systems. In order to react quickly to unexpected events, you need to know that something is going wrong.
In modern web applications knowing immediately when something is going wrong is vital in order to apologize to clients where necessary as well as fixing any problems.
Personally I find notifications via email the easiest (with backup via error log files), however many people choose to use exception tracking services such as Airbrake (previously Hoptoad), or Lighthouse.
I find Gmail combined with carefully written subjects is very handy as each exception is grouped along with similar ones.