I don't see how it makes a lick of difference. If anyone rolls higher than the Barbarian, they still can't act before the Barbarian (or whatever element is surprising the group), they may have their reactions available, as opposed to those who rolled lower than the Barbarian, but I'm just not seeing that as a meaningful distinction.
How are you not seeing that as a meaningful distinction? Your barbarian rolls 15 for initiative. The surprised knight rolls 16 for initiative.
The surprised knight can now use his parry reaction on round one when he is surprised. He has his turn on initiative count 16 of round 1, can't take any actions or movement, and then his turn ends. Next goes the barbarian who attacks him on initiative count 15, and our knight parries his attack.
If the surprised Knight had rolled a 14 or less for initiative, he could not parry the barbarians attack on round one when he is surprised.
You are arbitrarily and for absolutely no reason depriving characters of their ability to take reactions. If a monk roll higher on his initiative check even when he is surprised he can deflect arrows. Battle masters can parry or riposte. Wizards can cast shield or counterspell. Anyone with the defensive duelist feat can attempt to parry the attack. A bard that roll higher can influence the attack roll with cutting words.
And I mean it's not like you're saving any time because you're going to have everyone roll initiative after the attack anyway.
Just roll initiative. Then resolve actions in turn order.
I mean it's bad enough in this example that you would even let the barbarian attack with surprise. If I was escorting some NPC Prisoners out of a dungeon and you had them attack me with surprise, I would leave your game.
Making attack rolls outside of the combat sequence just makes it even worse.
I mean I just sit there and get attacked while you grin at me over the dungeon master screen and there is not a thing I can do about it.
I had some odious neckbeard do this to me in an AL game. A set of animated armour got surprise on me. Even though I clearly stated I was approaching it with sword drawn warily.
Said neck beard then proceeded to declare me 'surprised' regardless of the fact that I was clearly anticipating combat and was ready for it,
and rolled an attack on me before initiative was even declared. He then called for initiative... and happily advised me that I couldn't act on turn one because I was surprised. Finally on round three he allowed me to have a turn after the monster had attacked me no less than three times.
Even worse I was playing a warlock and had access to hellish rebuke.
The same thing happened in another game only this time with an ogre.
Along with Stealth, the surprise rules are one rule Dungeon Masters get hopelessly wrong over and over and over again.
The rules arent hard. Read them - Particularly if you are going to referee or Dungeon Master the game. Here; I will even explain them for you:- Roll initiative. If when initiative is rolled one or more combatants are totally unaware of any potential threats (totally caught with their pants down), then they are surprised and cannot take any actions or move on turn one. After their turn one ends they cease being surprised and can take reactions as normal (
including for the remainder of round one). They also are now also immune to the assassinate ability of any assassins in your party for the rest of this combat.