I’m not entirely sure who he should have put in the game there. At this point, Cora is just rolling the dice with whatever waiver wire dreck that the front office gave him to work with this week.
I'll push back on this one a bit, mostly because of what the bolded argument suggests.
Bleier was DFA'd - ergo, the field manager and his coaching staff were in communication with the front office, essentially saying, "We can't fix this guy, we need somebody else."
At the same time Lamet was not exactly lights out in Wor, but there had to have been some kind of communication with the Wor pitching staff, the FO, and the field manager as to what kind of pitcher the ML club needed and how Lamet was doing. Cora's role, in part, is to let the FO know what's going on with the pitching staff. Who is injured, or gassed, or responding to coaching, or developing a new grip/pitch, or whatnot, before it shows up in the game-data. (I'm sure this is an ongoing conversation from spring training onward.)
So there was agreement on Lamet as the best choice.
Then, once Cora has Lamet, he's just on the roster. The ML pitching staff can evaluate Lamet on their own instead of going to Wor, they can decide how best to use him (in conformity with what they asked to get in a pitcher, one supposes). This is all the handedness, splits, fly/groundball, K v. contact type stuff. It is also the "lets watch him throw and coach him" stuff. Which they're doing all the time.
So either Cora was part of a group that chose a fundamentally broken pitcher, or Cora knew he was going to be awful and decided to punt a 3-2 game, or Lamet just crapped the bed in his first ML appearance in awhile. (I'm going with #3 here, with a slight hint of #1.)
But the main reason I type all this is that the argument suggests a kind of a reflexive Cora v. Bloom false dichotomy we sometimes see here. Cora was intimately involved in the decision to release Bleier, promote Lamet, and use him in the specific game situation appeared in. Cora is not some passive victim subject to the whims of a detached front office that randomly sends him pitchers.