Pre-roll initiative

I've heard/read this idea a couple times. I think I'll bring it up to the group in the next session and see how responsive they are towards it.

Have initiative pre-rolled for monsters and players before the start of the game.

I see a few benefits of this:

1. Combats will take less time (maybe not by much but definitely some).
2. The flow from description to combat will be smoother. If the characters enter a room where the occupant won initiative, I can say "You see two orcs in battered armor stand guard in front of a door at the opposite end of the hall and the one on the left hurls his spear at you."
3. Related to #2. The players won't be as jolted out of character immersion and into game mode, every time I say "roll for init".

Monsters

During prep, I roll initiative for each potential combatant or combatant group.

Players

Before the start of the game, I have each player roll a dozen or so initiative rolls with all modifiers. I'll write them down in order then randomly determine what element in the sequence I'll use for the first combat and then continue the sequence from there. I do this in order to prevent the players from knowing exactly the future order. 

Example

For simplicity sake let say I have the players roll six times. The players roll the following in the given order.

Element #	Char #1	Char #2	Char #3
1	6	1	15
2	8	11	9
3	14	6	2
4	4	16	18
5	13	19	16
6	17	5	9

To determine the starting element I roll a d6. Say I roll a 5. So for the first combat the characters will have the respective initiative rolls:  #1: 13; #2: 19; #3: 16. The second combat the characters will have: #1: 17; #2: 5; #3:9. For the third, I warp around to the first element: #1: 6; #2: 1; #3: 15

Now to really prevent the players from knowing exactly the future order I would randomly determine the starting element for each player individually. But that is probably too much effort for added benefit.