For the record this is entirely my opinion though I'm kinda expecting to get downvoted for it, but I believe that cutting someone from the team was 100% the right decision and I believe that without it the team would not have improved or been motivated to start taking things seriously. When Robert shows up Blazer and Chase both say that the Z-Team has been a mess for a while, several months I believe, and that they've been causing a lot of problems. They've been bad enough that they've never had a dispatcher stay more than a few days. They aren't children they are grown ass adults and are subject to adult consequences. Whatever Blazer had tried in the past clearly wasn't working so they needed to do something drastic or else the program would get shut down. Because remember Blazer tells Robert as he's coming in that the program is at risk of being shut down.
People often cite Robert's speech as the thing that got the Z Team moving but if it weren't for the fact that there were real stakes and real consequences for doing badly, I think they would've just blown him off and kept acting how they did with everyone else. Remember part of how Robert got the attention of the team was by making it clear that he was there to determine who stays and who goes which forced them to listen to him. The cut forces the team to actually take things seriously and Robert uses that to light a fire under their asses to improve, which they did. And I think if they'd walked back the decision to cut someone after the second shift, it would've sent the message that they won't actually face any consequence, which could've undone the progress they made that day. The cut was necessary and they had to follow through. And it was done as fairly as it realistically could've been. It was determined by performance so someone like Malevola who is genuinely taking the job seriously compared to the others isn't at risk.
That's said, while I think Blazer is entirely right in her decision and I can even understand why she'd do it so early before Robert has a chance to become too biased in favor or against a particular team member, the writers should've had this be a "few shifts in" thing rather than a "day two" thing. Show the team being a disaster show why this is necessary. From what I've heard about the game's development I imagine there are external factors that made this not possible but I think it's a fault of the writing that this happened faster than it should've