There are two questions here in my view
1) What Euston is like in times of major disruption
2) What Euston is like in normal operation
For case 1, disruption I haven't had the misfortune to be there when this has happened but I could well imagine the concourse getting very crowded and there being crowd "crush points".
For case 2, its often very busy. The rise of advance tickets makes people like me be there well before my train time. I'm often there well before the previous train to my destination leaves. This is one factor generating a need for more space. Although personally I dislike it, the glass round the escallator from the underground does have the virtue of forcing people outside, then if the station is too full to get in you are alt least in space outside. It may not be nice but it's better than people coming up the escallator and having nowhere to go.
In the longer term, the HS2 station will add capacity and (hopefully) transfer some passengers to the new part of the station.
The only reasonably "doable" changes to Euston I can think of would be getting rid of the retail on the right hand side (looking at the platforms) and expanding the concourse and in the longer term adding a mezzanine over the ramps to the platform to create a second passenger space with travellators that deliver passengers further down the platforms.
Ticketing changes to reduce dwell times at the station might also help to a degree but given the need for reservations to get a seat I can't see this as an easy fix.
The Kings Cross rebuild is, in my view, very successful and personally I always use the upstairs waiting area for long distance trains.
As an aside, I've always found the Avanti ticket machines at Euston unusably slow. I've tries complaining about this but you get into a cycle of "who manages the station" complain to them, it's not their machine, go to Avanti and get nowhere.
In the end I had to get my advance ticket from the other machines (a different TOC) which were fine.
This is a symptom of the whole fragmented setup at Euston.