From the point of view of a coach, it really varies. As a coach myself if my team is absolutely annihilating another team, I do not want the game to stop. If we(my team) are all over them in the first 20 mins and we are scoring goals then I do not want that stop. Even more so if we are dominating and have not scored yet. Momentum is so important in a football game and by giving teams the chance to reset every 20 – 25mins it ruins the chance to build and build momentum. Momentum is also very fragile and something as little as little as a couple minute stoppage can change it or break it. That’s why you see teams who are under pressure start fouling, they do it to disrupt and slow the game down to slow the momentum of the other team.
That works both ways though, if I was a coach and my team was getting hammered, I would want the game to be slowed down and as many interruptions as possible to disrupt the other team. In this situation 4 quarters would be a benefit to a coach.
It would also be easier in my opinion to close out quarters instead of halves. If a less skillful team is winning a game or perhaps drawing a game it is easier, in my opinion for that team to hold on to that advantage. This is because instead of holding on for the last 30 mins of match for example they would only have to hold on for 3 minutes and then get a chance to reset and recover. 4 quarters would mean potentially more upsets, games would be closer but slower and, in my opinion, more boring. People watch a sport like football to be entertained and for me entertainment is action, by slowing the game down you rob football of its action and make it more pragmatic.
So, no I do not think that football will ever go to 4 quarters, even if it did it would not be for the for see able future.