bbPress and WordPress Search

It looks like when bbPress forums are installed the default WordPress search form does not include results from bbPress topics and replies. I think it would be nice to have an option to use the WordPress search to search into bbPress forums, topics, replies.

For example, if a user has a content rich site with different section for forums. People searching on the site will not be able to see forum topics and replies matching the search term. To allow users to search into forum topics and replies, one needs to either add bbpress search widget or some other custom solution.

I do understand that this might fall into plugin domain, there are a couple of plugins that do that. But I feel that there should be some way to provide, either:

1. bbPress search widget with an option to enable search WordPress posts, pages, and other custom taxonomies as well.

2. WordPress search widget with an option to enable search for forum topics and replies.

Something like this:
https://goo.gl/WDrbF9