Obviously, whatever you say is happening at your table with brainiac is nothing I can speak to - but if I were told by my players that my encounters were boring and predictable, the last place I would go for solutions would be to change " when we roll stuff."
I really would not think that random order of events makes a significant change in the overall statistics of the outcomes... but let's say it does.
What you are saying then is that the initiative rolls round after round are a bigger impact in the outcomes than the characters and the player's choices were?
If that were the case in my games, I would see that as a flaw and a problem - not a feature to be lauded. I want the characters and the players choices yo be the biggest most meaningful factor, not the initiative dice.
When you drive to work in the morning, you make a lot of decisions right? Where to walk, what lane to drive in, where to cross the road, how fast to drive, where to park... right? You are in control of much of it right? But I bet you can predict pretty well exactly what time you will get to work every day. Especially after 30 years of going to work. Even if you change jobs, or get a new car, or a new bus-line or subway opens you still can predict pretty well when you will get to work right?
The things you have no control over, an accident or break down or other people have a bigger impact of when you get to work than the decisions you make. It's not because you don't have control. Its not because the choices you make are not meaningful; it is simply because of all the choices you make are optimized to get you to work. Sure, you could make a different choice, and take longer to get to work, but why would you do that?
I've been playing D&D and other tactical and strategic games with this player for about 40 years now. There is no reason he is not going to make a combat choice that is not optimized (unless he chooses to role-play a character that would do otherwise). Most of the rest of the players are not going to make a choice that is not optimized (unless it is in-character). As the DM I'm going to play the NPCs/Adversaries in a meaningful way. Usually that means close to optimized, but not always.
Then think about a combat, you really can break it down to X vs Y and various types of combatants; melee, ranged, tank, control, buff, etc (whatever names you want to give them). Then you have locations like open area or ones with cover and traps and hazards. All of those are just factors that can be accounted for in an optimized solution.
If your brain works in a way, and you have played ten or hundred of thousands of scenarios, you can "see" the likely outcome before combat begins.
I know, I know, you are going to tell me to mix it up. And I do. But, another one or two predictable variables like terrain, etc are just more factors. Even re-rolling init is just another factor. More factors, more complexity.
The biggest things that "cloud" the predictability is randomness that does not average out over the length of a combat and unknown enemies. Re-rolling initiative is something that yields highly variable results given the short number of data points in a combat (i.e. half a dozen rounds). Even the PC with advantage and +7 initiative doesn't always go first or even in the top half.
To reiterate, it is the players choices that have the biggest impact on success and failure in combat. But it's because they have to account for the randomness and chaos of combat. Not because the players are not experienced enough to make optimal choices. The players get to make the choice, do we play it safe and heal the paladin, or do we take a chance that next round I might go last and not be able to heal him before the BBEG gets a lucky hit if I fail to paralyze him this round?
