The issue with passing on this responsibility to senders is that every major Internet Messaging app needs to implement it, we cannot just create an IM app with this features as there is a huge 'chicken-and-egg' issue for any new IM app i.e. chat app requires significant adoption to sustain, people will use it only when their friends and family start to use it; besides the problem we could potentially address with such an app is not a majoritarian opinion.
At-least text(SMS)/Calls has a standard telecommunication consortium(GSM), but it's not an easy task to implement and force adoption. e.g. RCS (Rich Communication Services) the successor to SMS has been under work for over a decade and it's just slowly being rolled out in US in Android.
Besides, I think existing apps would lack the will to implement any such measure as more notifications = more usage; goal of Business is to increase the usage of the product, rather than restrict it.
The best available option to those of us, who see this problem is to build a notification manager which intercepts notifications and uses NLP for parsing each notification for scheduling it according to our priority.
The best available option to those of us, who see this problem is to build a notification manager which intercepts notifications and uses NLP for parsing each notification for scheduling it according to our priority.