I believe that splitting movement and attack into separate rounds does not actually solve any problems, other than having individual player 'turns' come faster. However, the amount of time that will be spent all told will not be any less. Whether you move and attack at the same time, or move and attack with two minutes between them (while other PCs go)... the amount of time actually doing your actions of moving and attacking do not change.
And in fact... it might actually take longer, because the smaller you break a player's action segments up... the more chances you have of having players not paying attention to what's happening on the board and thus needing to spend more time flipping through their sheets deciding what to do when its their turn. If you have move and attack together... the player will look through his options for both at the same time. Whereas if you split them up... he'll spend some time ramping himself up to find a move action (or equivalent) on his sheet, then next round spend time ramping up to find an attack action on his sheet. It's like traffic lights: the longer a light stays green, the more cars can get through... because every time you have to get cars ramped up from a stopped position to finally moving takes more time and slows down the entire process, resulting in less cars getting through the light.
The only real way to speed a player's actions up is to lessen the amount of options a player has to choose from on his turn. The less options he has... the less hemming and hawing he has to go through to determine what would be the best tactical decision to make... and the faster he can choose something and just do it. Thus the reason why high-level games can get so unwieldy is because there are just too many options for a player to look through and choose from: 2-4 daily powers, 3-5 encounter powers, 2-3 at-wills, 1-8 magic items with abilities, 2-10 feats with power options... each PC has a sheet of like 10 to 20 things he needs to look through each and every round. THAT'S what takes so long.
(The irony being that it is a common refrain from many players here on ENWorld that they wish feats did NOT give just static numeric bonuses because they aren't 'exciting' and the possibly increase game unbalancing... and yet those are the most helpful ones in terms of speeding up the game, because the numbers are automatically baked in and thus its one less option for a PC to think about and consider on his turn.)
And in fact... it might actually take longer, because the smaller you break a player's action segments up... the more chances you have of having players not paying attention to what's happening on the board and thus needing to spend more time flipping through their sheets deciding what to do when its their turn. If you have move and attack together... the player will look through his options for both at the same time. Whereas if you split them up... he'll spend some time ramping himself up to find a move action (or equivalent) on his sheet, then next round spend time ramping up to find an attack action on his sheet. It's like traffic lights: the longer a light stays green, the more cars can get through... because every time you have to get cars ramped up from a stopped position to finally moving takes more time and slows down the entire process, resulting in less cars getting through the light.
The only real way to speed a player's actions up is to lessen the amount of options a player has to choose from on his turn. The less options he has... the less hemming and hawing he has to go through to determine what would be the best tactical decision to make... and the faster he can choose something and just do it. Thus the reason why high-level games can get so unwieldy is because there are just too many options for a player to look through and choose from: 2-4 daily powers, 3-5 encounter powers, 2-3 at-wills, 1-8 magic items with abilities, 2-10 feats with power options... each PC has a sheet of like 10 to 20 things he needs to look through each and every round. THAT'S what takes so long.
(The irony being that it is a common refrain from many players here on ENWorld that they wish feats did NOT give just static numeric bonuses because they aren't 'exciting' and the possibly increase game unbalancing... and yet those are the most helpful ones in terms of speeding up the game, because the numbers are automatically baked in and thus its one less option for a PC to think about and consider on his turn.)