Given 10-15 second rounds it would be possible to change actions in response to what is happening during the round.
Sure, if "change my mind" is treated as a fast action.
Everything is happening within that 5 - 10 seconds, and everyone's actions fill up the available time. Really, everyone is acting simultaneously, in a noisy and confusing situation. Initiative is a game contrivance that resolves the conflict over who shot first when two characters act against each other, and also keeps everyone from speaking at the same time. Changing your mind based on another player's actions is at heart a form of metagaming, which (a) allows groups to be more effective than they really would be and (b) eliminates the comedy of errors that occurs when everyone tries to do conflicting things at the same time. I don't worry too much about (a) but the loss of (b) is disappointing. But what to do about it?
I get the intent of the suggestion re initiative cards but drawing new initiative every round and declaring your intentions at the start of the round slows things down. Also, it doesn't really solve the problem. When Bob says, "I'm shooting the guy with the RPG," I can still change my mind before I speak, so we haven't fixed anything. Having players write down what they plan to do gets rid of that but also slows everything down. I think most groups want to keep things fast-moving. I think also that most people aren't too concerned about this. To me the best solution is just to set a shared expectation for the group & then go have fun.
As an aside, when you get that coordinated action -- Bob kicks open the door for me to throw a grenade -- there should have been some kind of communication to coordinate this. A few shouted words is a free action but to communicate and agree on a plan should be treated as a slow action, eating up a round. It's a pet peeve of mine when people have conversations during a firefight and pretend they took no time at all.
