Earlier quoted context omitted.
Good suggestion. An RSS feed sort of exists already, and twitter is just a better vehicle to deliver these alerts. We could try to throttle ourselves, and better filter e.g. duplicates, that is true.
I think if the focus is mobile you can try setting up a very lightweight page with the latest events (with a cache in front, something that is updated every 1min or maybe 5min should be enough)
They need to meet their audience where their audience can meet them. Just about every phone nowadays can access Twitter in an immediate and obvious way. Twitter will meet their audience where their audience needs to be met.