The short answer to this question is No, LibreOffice does not come with a dedicated email client program. However, if your needs are basic (such as sending personalized emails via mail-merge or sending documents as emails), LibreOffice does provide a workaround to solve this problem.
I have already written a few tutorials on email-related queries in LibreOffice:
How to set up the outgoing SMTP email server: This is the first step required to connect your email server with LibreOffice. Thus, when you use the email sending feature, it connects with the SMTP server of your email service provider and sends emails in the background. However keep in mind, LibreOffice does not support reading incoming emails; it can only send emails.
How to send documents as email: In this tutorial, I have shown the steps by which you can send your document as an email attachment directly within LibreOffice without leaving the program. Though, you need to first set your default email client in LibreOffice.
Now coming to the main question, Why doesn’t LibreOffice include an email client?
Being an open-source software, the development of LibreOffice is entirely run by volunteer efforts. Hundreds of developers, coders, and technical writers around the world come together to build and provide users with an open and free alternative to the proprietary Microsoft Office.
Due to the very nature of any open-source project, it does not always have sufficient funding or manpower to implement all the components that could be otherwise fulfilled by integrating with other third-party open-source programs. Therefore, it is wise to focus on providing a comprehensive suite of office tools, rather than specializing in a specific area like email management.
For example, where users of MS Office are used to experiencing the tight integration of Outlook email client with MS Office suites, LibreOffice also has a similar integration by supporting third-party email clients. And Thunderbird (Evolution, K-mail, and others if you’re on GNU/Linux based operating systems) is the number one choice picked by many avid users of LibreOffice.