We used to do this back in the AD&D days, but we stopped and went with initiative being rolled at the start of combat only once, keeping the order for the entire combat, but allowing characters to lower their nish if they want (if everybody wants to go at the same count, then they go at the slowest nish rolled).
Here's why we don't re-roll every round any more (not counting the speed of the game picking up with the fewer dice throws):
Able wants to fire at Zarl. Zarl is 30 feet from Able when Able decides to shoot at him. The GM says that Able must take a round to ready his bow (pull it off his back, quickly string it, and ready an arrow).
Zarl says he's going to run back to his tribe and get help.
Roll initiaive. Able wins.
Round 1.
Able readies bow.
Zarl increases range from 30 feet to 150 feet.
Roll initiative. Zarl wins.
Zarl increases range from 150 to 270 feet.
Able fires at his target, now at range 270!
See the problem here? Zarl moves 240 feet in the time it takes Able to ready his bow and fire.
Zarl is very fast to have moved 120 feet in one round!
If you rule that a character needs a full action to ready their bow (because they need to string it — makes sense, but most tables allow drawing a bow much like drawing a sword, which is to say, free object interaction) — and Zarl is not equipped with a well above average speed of 60' per turn, you get:
Round 1.
Able goes first, draws and readies his bow.
Zarl dashes 60', increasing range to 90'.
Round 2.
Zarl goes first, manages another 60', increasing range to 150'.
Able gets a shot off. Zarl is still within normal range of a longbow.
That seems reasonable enough. One can certainly manage 120' in 12 seconds — that's 40 yards — and, if Able needs 6 seconds to string his bow, he might need another few seconds to take aim. Meanwhile, Zarl is still running as the arrow takes flight, so Able needs to lead Zarl a little bit. By the time the arrow hits Zarl (or misses), he has made 120'.
Meanwhile, a decent high school track athlete has covered 100 yards, or 300 feet.
Initiative every round definitely adds die rolls. But I don't think it challenges verisimilitude any more than locking all characters into a fixed action order.
--EDITED TO ADD--
Never mind the fact that, in the above case, if we just have two characters and Zarl is definitely just stringing his bow for a round, I wouldn't even bother to roll initiative on the first round. The order of resolution is irrelevant.
The fiction, even in your case, where Zarl is dashing at 120' per turn, is quite easy to imagine.
Able and Zarl see each other. Able draws his bow and quickly begins to string it. Zarl takes a second to react, but turns to sprint. (If there were any other characters for whom Zarl's low initiative roll mattered, his late reaction might allow them to get a shot in at closer range — say a javelin.) Zarl is a trained runner, wearing only light clothing and on a good, firm surface. As Able finally raises his bow, Zarl is in a full-on sprint. Able hesitates, trying to gauge the speed of his opponent to properly lead the arrow, before letting an arrow loose.
As I've said earlier in the thread, I view initiative as being intrinsically related to the resolution of
simultaneous actions. It's not Action A.1, Action Z.1, Action Z.2, Action A.2. These actions are occurring simultaneously, as well as other, minor actions that we don't bother to model exactly. The initiative just allows us to determine which outcomes get resolved first, in cases where the outcome of one intended action would override the outcome of another intended action. (So, again, in the case of Zarl and Able, the first round need not bother with initiative, because the timing of the outcomes have no bearing on each other. Able can string a bow in 6 seconds. Zarl can sprint 120' in 6 seconds.)
You can, of course, use the Speed Factor rules to apply some more fiddly verisimilitude onto these rolls. Different actions get bonuses or penalties to their initiative. For instance, we give an initiative penalty to any characters who are drawing a weapon or otherwise shifting equipment. The problem with the Speed Factor is that this
definitely slows down the initiative rolls until your players start to memorize the fiddly bonuses. I don't DM every week, so we haven't used it recently.
Anyway, as Hemlock said in his post, the reason I like the declare and then act approach is that it allows me to create a seamless approach to actions both in and out of combat. Out of combat, it encourages players to think of their characters as individual actors within a room, while also making sure some of the more shy players get spotlight time. It has a natural way of shifting the attention from one PC to the next. It also makes things like aid another or guidance more meaningful. And it really helps to preserve that sense of, "meanwhile, where Player B is standing, something else is happening at the exact same time."