It is true that a match can change. This has happened to me before. Not once or two times but plenty times. You can even see the match change around 80 to 90 minutes. Some matches may even not change but the opponent may just have a tiny opportunity which they do not misuse and just score. The score can even happened at the 3, 4, 5 to 10 minutes extra time give after 90 minutes to conclude the match as 90 minutes.
You mentioned last-minute, heart-stopping incidents. Last-minute goals or extra-time miracles? Don't they disregard all statistics? Statistics are useful, but unpredictable variables limit their applicability
You know how statistics work
But interestingly I think some of the variables like you mentioned (weather changes, injuries etc.) will be considered with new AI based models in the future. We are not there now (I think), but AI could scrape the data from the Internet and then adjust odds before the game starts based on any new information gathered and the calculated impact it may have on the game.
But placing bets during the game can also be fun. I guess most here know what kind of situations in a game can be an indicator for a turn around of one team or other important events. That's why I usually try to have some funds on the platform to make a quick adjustment bet if it seems to be appropriate to me. But there will remain a factor of coincidence that not even improved AI models will ever be able to predict.