I fly almost every 2nd week for work, so I see those issues too.
Personally, I completely ignore the announcements. I have my headphones in anyway most of the time.
I have found the screens to be pretty up to date and they are quite a few. Especially if you have access to the lounges.
The Geneva airport, from which I fly most of the time, has actually a pretty good app where you can scan your boarding pass or add your flight number and it will push updates to your phone.
This has been really useful.
What does really bug me though is that with some airlines, their loyalty programs have grown completely ridiculous. They will have teared boarding for Platinum, Gold, Silver, Ruby, Sapphire and so on. This really slows down boarding and people are confused as to when they should board and what line to line up at.
My former employer TEAGUE is doing some interesting work around this after they re-jigged as a design agency focusing on travel.
There project Poppi has some interesting ideas touching on those stress points.