Choice of user front end should be local user selection not something enforced by tool. Message should be send to a db and how each user selects to receive it and respond to should be only his local matter.
One at some time of the day may prefer email, some like web interface like slack, some like chat etc .... a bit later he may choose to adjust the front end such that say after hours messages to him go to email vs live chat.
Today all tools have a globally unified front end which by design is a fundamental mistake.
Best,
Robert.