Simplicity vs. interesting(?) decision in turn order

Weekly updates:
I keep playing games and coming up with abilities.  I want to have 5 abilities per character type (i.e. melee, archery, spellcaster, etc), and I'm almost there.  

For today, I want to talk about the initiative system.

Illeria has an I-go-you-go system, where each round, players take turns acting with one character at a time (until all characters have acted).  To determine who goes first in a round, I have had players roll a dice, and whoever rolls highest gets to pick whether go first or second.  If there are ties, then you reroll until someone wins.

I had a funny moment when I was playtesting by myself.  For a long time, I did this faithfully, rolling two dice, picking the highest, and then deciding when the team that won would want to go.  However, at one point I realized that because this is a zero-sum game, and I had all the information, I there wound never be a situation where one player wanted to go first and the other second.  So, since it came down to an even split to decide, I made it easier on myself, and rolled one dice, with each side having a 50% chance of going first.  This meant I didn't need to think, and that I never had to reroll ties, and gave the same outcome.

This got me thinking, should I bother making whether to go first or second a choice at all?  The main pro is that the player who rolls higher gets to make an interesting decision.  It is also more what players expect.  The main con is that it is one more step in the game.

Thinking about it, if you just flipped a coin each round to determine turn order, that would take 10-ish seconds.  If both players roll a dice, that also takes 10-ish seconds.  However, there is also a 1 in 6 chance that they need to reroll the dice (making it 20 seconds), a 1 in 36 chance they need to reroll at least twice (30 seconds) and so on.  This should take an average of 12 seconds (see here).  Plus, there is the time a player needs to think (another 5-10 seconds), and the more squishy impact of cognitive load, perhaps on something other than what the game should be about.  Is this decision worth doubling the amount of time it takes?

I was leaning towards "no", that I should just make it random, but then had another realization, which is that I don't need to make the odds 50-50.  When I initially designed Illeria, parties had a leader, and if the leader died, their party suffered a penalty to dice rolls.  I don't know if I want to bring the leader back, but I have had some other ideas of how to tinker with the roll.

First, players could get +1 to their roll for each character who is knocked out.  I'm really liking this, because it would produce negative feedback.  Wargames are notorious for having positive feedback loops: you win by killing characters, and killing your opponent's characters makes your opponent less able to kill your characters.  I've often struggled with this, and it might be a way to do it.  

Second, each player could spend Energy Points to boost their roll.  This would add an interesting decision.  Additionally, near the end of the game, parties sometimes get to a point where they gain Energy Points faster than they can spend them.  This could potentially remove that, by giving an infinite pit that you could throw points down.

I really like #1, and am on the fence about #2.  They will slow things down, especially #2, though I also have ideas for eliminating ties (the player who lost last time wins ties).  I think I really need to just playtest this with others.  But, if these extra rules feel like one extra rule, I think I'll just go full simple and make it a 50-50 chance that each player goes first (no decision required).