When Acrobat communicates with your default email application, Microsoft Outlook, it does it through Outlook API (Application Program Interface) and not the User Interface (UI). The use of your default signature is automatic when you create a new email through the User Interface.
Acrobat can communicate not only with MS-Outlook, and even considering Outlook there is more than one version of it, so I don’t know how difficult it would be for Adobe to insert the Outlook default signature when sending a PDF by email from Acrobat, but I agree with you, this would be useful.
You can request this feature in the following link, if many people request it maybe Adobe considers including it in next version or update: https://www.adobe.com/cfusion/mmform/index.cfm?name=wishform