The transition from round to round is arbitrary. You get shot at the same number of times across the NPCs all getting one turn no matter where your turn lies in relation to them. You go, they go, you go, they go. Or they go, you go, they go, you go. There is no they go, you go, you go, they go. Deliberately. It's not change blindness.
This isn't technically true, SSDR, unless I am completely misreading the initiative Edge Boost.
My initiative score is 21, yours is 23. On the first round, you go first, then I take my turn. Then, at the start of the next round, I spend an Edge to boost my initiative to 24, and go again. You go, I go, I go, you go. After that point it returns to the alternation, but you could do the same thing to me at a later point.
Technically, if you want to achieve a situation where you go after a friend who rolled less than you on initiative, you could do that under the current rules, but you don't take the action your friend does; they boost their initiative to beat yours. Of course, that could cost a LOT of Edge, with lots of people turning in their own Edge two for one to give it to the friend. But under the current system there is no way to choose to go after an enemy that I can see.
Also, in a lot of cases an equivalent tactical situation can be achieved when you consider that going later in the current round might be practically equivalent to going sooner in the NEXT round. But that won't always be so, and again it might cost a lot of Edge.
EDIT:
Say two fast-acting PCs are fighting three slow NPCs. PC1 wants to wait for PC2 to do something before attacking (see my previous post for some narrative reasons this might make sense.)
Sorry, I'm on a roll here, but if PC1 can totally go after PC2 if he wants to, PC2 just needs to boost their initiative. That is, PC1 and PC2 can coordinate to make that happen if they have enough Edge and the difference in their initiative scores is not too large.