Not present, or handwaved away? If your players approach it as a game and just accept the rules as being what they are, that kinda handwaves away any problems or issues. But if you've got players who want to dig deeper into the rules and-or realism of it all (which is what I'm used to), then issues like this will inevitably rear their heads.
I said not present.
Here you are doing it again. You're assuming that my players and I are either mistaken about what's happening in our game and/or how we feel about it, or that these problems exist and we just ignore them. That we don't take the game as serious or are less concerned about realism than you and your players.
That is nonsense. Stop doing that.
I'll try another way to explain.
None of my players think that "initiative order" is a very "realistic" thing. They accept it as a need for the game to work, and so that's where it matters. But in the fiction... in the make-believe stuff that's happening in the game... my players and I realize that initiative order means jack, and we accept that there's a lot blurring of things... there's a lot of action happening that's not specifically noted or tracked. For the fiction, initiative is much less rigid, and just a rough approximation of the major events of the fiction.
For instance, no one I game with thinks that a trained combatant will only make one attack on his opponent every six seconds. It would be silly to think that. Six seconds is a very long time in situations like combat. Instead, they accept that the single attack and damage roll is meant to represent the ongoing battle. They understand that when a character has taken 40 points of damage of their 90 HP, they're not ripped to shreds with multiple wounds... because hit points are representative.
It's the same for initiative order. Reactions and readied actions can disrupt the standard order of initiative because that's what they're designed to do... to emulate the parry or counter, the response to an action in an attempt to thwart it.
This ability to separate the order of operations of the game from the order of events in play is what makes the fiction more realistic for them. It is not "hand waving" anything away or "twisting the fiction"... it is a different way of looking at it.
Frankly, I'm surprised you're so resistant to it since you said you'd like for the game to have as little impact on the fiction as possible.