Ticket system for initiating correspondence?

Question

Technical support

Has anyone come across a ticket system capable of initiating an external request with a user-friendly interface? If yes, please tell me the name.
It is necessary that the first letter be initiated from the ticket system and subsequent correspondence be conducted within the framework of the created ticket.
I googled the most popular ones (OTRS, osTicket, Freshdesk, etc.), all are aimed at working with the incoming flow of applications, but not many work in the opposite direction, and even those that work do not leave a pleasant impression.
Both freeware and zabubble systems are interesting.