I have a good amount of experience in customer support as well, via Discourse (and other forums), email, and the like. I certainly agree with/share many of your concerns! That said I think these are broader general problems, and apps like Slack still have not solved the issues with e.g. @ everyone except by just putting a warning when people try to do that (or disallowing certain users/user groups from using it at an admin level - this is not something individual users can control), so I’m not sure we can expect Discourse to be able to do a better job here.
You can, however, control your notification preferences (e.g. whether you get notified if someone @ everyone, etc.). So maybe that’s an option to consider, if not already part of the notification controls being provided by Discourse and with the integration of the new chat features into that.
Anyway, my overall point is that you are describing some large and very real problems, but they are problems that basically no other tool has fully solved to everyone’s liking. This is certainly in part because it’s a really hard problem. I think it is unrealistic if not a bit unreasonable to expect the Discourse team to address many of these issues as a core part of chat design, it feels like something of a “feature creep” to me. I do not, of course, speak for the team in any capacity though. 
Having said this, I do also hope they come up with some great ways to let people manage their mentions, notifications, etc. that are easy to use, congruent with Discourse design, etc.