I was stood next to an elderly fan at the Carlisle game in 2007 when we were League 1 champions. 10 minutes in he collapsed suffering a heart attack. Getting the attention of the St Johns’ responders let alone the club doctor was very difficult. Fortunately we were on the terrace so people could make space easily (would have been impossible in the seats) but you still had people nearby reacting the game and moving around whilst we were performing CPR. Stopping the game would have helped get medical assistance across more quickly and might have helped fans nearby realise we needed space.
So whilst it can be annoying, I can understand why it’s now standard protocol in these circumstances.