Or may be just search the title and all custom fields?
Using just the title is very limiting as you will need to use keywords on the title to get a match. While, as a search, it should be broader and do the search in the post's content.
In my use case, I have a post type as a links library, with the post title being the actual link, with extra information added as custom fields. And it will be hard to add links out of the title using the Post field.
Any workaround to at least switch the search from targeting the title to a specific custom field on the post?