Explain a scenario where the use of $watch in AngularJS controllers for data binding might lead to performance issues.

Using $watch in AngularJS controllers for data binding might lead to performance issues in scenarios involving large arrays or collections. When monitoring extensive data sets with $watch, AngularJS has to constantly check for changes, which can be resource-intensive. This can result in decreased performance and responsiveness, especially in applications dealing with substantial amounts of dynamic data. Recognizing the limitations of $watch is crucial for optimizing data binding in AngularJS applications.