Yeah, I just always thought such a system might work real well especially in a video game. I agree that chaos of battle might mean you fire an arrow at a target and then they die before you hit. That's true. Besides this, the pause thing would slow the combat down anyway. Probably better just to let it go.
As for initiative every round and weapon speeds, you wouldn't even need that with what Im suggesting. Everyone picks their moves and the game has all characters move at once.
So let's say Lae'zel selected the Gobbo Berserker with melee but Gobbo berserker picks my main who picks the Captain. Captain chooses my main with a bow. Initiative order for the combat was rolled and order is Lae'zel, Berserker, Main, Captain.
When round plays out, all combatants move. Lae'zel intercepts Berserker on his way to my main within 3 seconds. She has higher initiative and swings. Berserker continues after main. Lae'zel follows and gets Attack of Opportunity because he's continuing after my main without Disengaging. Berserker reaches main just as main reaches Captain. Berserker has higher initiative. Berserker swings before main. Main has higher initiative than Captain, so main reaches Captain and swings and puts up Shield of Faith. Captain was too slow to get a shot off before main got to him, so now he fires at my main when my main is point blank. Sucks to be him. Now it's harder to hit.
Next round, same initiative order. Captain uses disengage to escape. Berserker attacks Lae'zel. Main attacks Captain. Lae'zel attacks Berserker. Round plays out. Captain immediately starts to run away causing main to pursue. Lae'zel swings first but misses. Berserker gets AOO on main. If Lae'zel had killed him he would not have gotten AOO because she had higher initiative. Captain continues to flee with main in pursuit. Berserker turns and swings back at Lae'zel. Main swings at captain as they come to the end of their move distance.
It might be tricky for the PC to calculate how all this would work, but I think it could be done and could be fun. Would speed up combat too but give players more control than RTWP and would cut out the need to spam Pause during combat constantly.