Consideration should be given to joint departure boards at St Pancras and Kings Cross covering both stations.
I think that's a good idea, but I also think they'd have to consider the time some people will take to go from one to the other.
Let's imagine someone needing to use a lift, and not being so able bodied. The lifts for the low level platforms at St Pancras are incredibly slow, and then you have the trip over to King's Cross and,
potentially, a trip to one of the low platform numbers - possibly even platform 0.
It may well cause more problems than it solves as it could easily take 10-15 minutes for some people, and a solution to remove trains in advance will also likely anger people who will say they
could have made it.
At the end of the day, a LOT of people are going to be rather annoyed that they can currently arrive at King's Cross and if they aren't too late, can stroll to the platform and get on an empty train. Most people use their phones to see what platform to go to and while that can catch some people out, and cause hassle to platform staff and cleaners, generally it's quite relaxed.
Compare that to fighting amongst others on one single platform, and having very few areas to sit.
In the reverse direction, we have people now able to potentially travel through to the core, but in reality the need to currently walk over from KGX to STP isn't such a big deal as for the most part if you're going to Farringdon, City Thameslink etc then you just take whatever train comes in.. For that bit, it's like a turn up and go tube service.
I am sure as time goes on, many people will wonder why it was necessary to link GN up to the core if things regularly fall to bits. Many people are more likely going to travel to Finsbury Park to get services north as you have more trains and options. Once the station is more accessible the only issue will be the exposure to the elements.