There's nothing wrong with testing your skills against an adversary with the goal of winning - that's the point of dueling after all, but because of this natural tendency of our ego wanting to 'win', any free flow partner practice can turn into a competitive sparring match without much effort whether intending to or not.
If 2 people are free flowing, often one will enter when they see the first opportunity, and because entering itself creates an opening in the attacker, the other takes that as their opportunity, both parties end up attacking together and both generally 'die'.
A series of glorious double deaths is a sure sign that neither party is learning anything useful anymore, just how to throw their lives away. One is attacking rashly and trusting to luck, the other is only seeing the opening not the consequences. (Please read George Silver's rant about this all the way back in 1599 to see that it has been a long standing problem - Monkey Dancing with it's non lethal format + bladed weapons, which by their nature are lethal = not a good combination.)
But how to progress past this?
It seems like you need to create a format to practice in context, but without the need for the ego to always win. (Technically I would not call dying 'winning' .... but it seems that getting a first hit on the opponent equates with winning in our heads regardless of the consequences. Apparently the monkey ego is not that smart ....).
If you are familiar with Rory ConCom material and can 'de-escalate yourself first' from an interaction, you can pretty much play and generate progression with anybody, the problem is when neither party can escape from the dance.
I've found 2 ways to work past this (there are probably more) -
1) Assign different tasks to each party - one is the initial attacker, the other the counter attacker, let each person 'win' or succeed at their game for a while, then add a counter from the other side to the game ... then add another level of difficulty.
Example - A cuts at B who does not defend
B tries to defend against the cuts (without hitting back)
A adds faking and timing to trick B
B keeps trying to not get hit
B gets to counter, but after A's attack only
A tries to cut B then evade/block the counter
This game can go in many directions:
A cuts at B who does not defend
B hand tags A as they attack
A tries to avoid the hand tag and still cut to B's body
B hand tags but also tries to evade/block the attack
Narrowing the parameters this way focuses the game and seems to take away the need to impose status.
2) Start the flow with a question that needs investigating. E.g. "How does using a cane change the dynamic if you are fighting a short sword"? or "What happens if I only counter strike"?
Now both parties are on the same side trouble shooting a question, not adversaries in a contest.
Neither of these are permanent training formats, each individual has to learn for themselves how to not get caught up in their ego if they want to progress, but at least they can facilitate an exit from the loop.