Most fights I have end in 2 passes unless the mage decides that mandatory naptime is worth gordian knotting the whole thing. It may be because the meta I play in values full defense extremely highly and so players are reducing their own offensive power, but I find it strange that PCs are consistently able to clear a fight in a single pass even though SR is pretty darn good about ensuring PCs can't down more than one enemy a pass. Even vs grunt corpsec it generally will take a team of 5 players in an environment as optimized as the reddit LCs to take down a group of enemies slightly larger than them unless literally everyone is a samurai. "Initiative is king" has been seen as a pretty uncontroversial truism for every edition, so I hope you aren't offended when I say it seems like something is creating an extreme outlier scenario if your group is able to clear fights with one action per-player. Do you not use NPC edge?
Another big advantage to edge in SR5 was stalling: if you had the initiative advantage it meant defensive action played extremely in your favor: Your opponent had to either expose themselves or allow you to get a series of turns without them being able to react. This was especially potent because you also immediately get to act again even after you run out of initiative if you are the highest, meaning the turn rotating gave you two actions in a row, allowing you to do very dangerous things like flank with total impunity or play around with AOEs when no one could Run Like Hell. It is very very VERY good to go fast in SR5. A single pass advantage creates by a 1d6 therefore could translate into a two pass advantage with a back to back bonus, while in SR6 you aren't even able to get one effective extra pass with a single d6. There is a danger if you allow multiple movement actions per pass via minor actions of similarly stacked double turns exploiting the inability to react, but hopefully they aren't allowing that because those would be silly even without bonus majors.
That said, this isn't a PVP game, and one player getting two attacks at once has different effects in a cooperative game either way. That means that we don't actually have to worry about if it is fair to be exposed to high initiative attacks at all, as long as it is rare in the hands of NPCs.
Specifically, because majors are a player's ability to impact a combat offensively, they don't factor in to your 'time to kill' and thus wouldn't affect NPCs attacking you at all. You are dictating how many NPCs you can attack. You won't die any faster or slower at low initiative dice, so as long as the essence buy in is non-trivial, you don't need it. That said, currently in 5e most every non-magical PC makes a point of using Jazz or buying an initiative booster, so even if it were mandatory, that is still the status quo. While obviously I didn't put a ton of thought into it, paying 3/4ths of your essence to attack 3 times in combat isn't actually that attractive unless 'ware overall gets dramatically less useful. There is a reason why even in two turn fight metas you aren't seeing a lot of move by wire PCs, making your turns more impactful is equally as important as more initiative.
I fear the current system will actually make investing in initiative totally worthless, as minor actions as we saw from the lets play are not actually that useful and are not attractive enough to incentive you towards making extreme sacrifices towards getting them, which is why people are wondering if wired reflexes is going to be dropping to a sub-1 essence cost per rating item.