There’s no support for the second rationale being “more widely accepted” than the first. Although the author does note that the second rationale can support intuitions against overly harsh punishments, this doesn’t imply anything about the level of acceptance of the retributive rationale. How many people accept it compared to the number that accept social-benefit rationale? We don’t know.

Supported. The first rationale doesn’t allow for considerations of what’s appropriate, whereas the second rationale does. So the second rationale doesn’t have the “same” potential unfairness — if a punishment is too harsh, the second rationale can support an argument that it’s not just.

No support for “more kinds of punishments.” “Kinds” of punishments involves the different ways in which people are punished — jail, fine, sex-offender registry, execution etc. The passage doesn’t suggest that the second rationale justifies a greater number of different kinds of punishment than the first rationale.

Not supported. The second rationale can justify the intuition that certain punishments are overly harsh; but this doesn’t imply that the second rationale is used only in these cases. One can apply the second rationale to more moderate punishments or even those punishments that barely cause any harm to a criminal. The second rationale might be used to support punishments that don’t go against our intuitions.

Not supported, because the first rationale can allow for punishment that is equally lenient, as long as social benefit justifies lenient punishment. Although the first rationale allows for harsher punishment than the second (because the first rationale doesn’t consider proportionality), that doesn’t imply the first rationale can’t also allow equally lenient punishment as the first. In other words, the first rationale might have a wider range of allowable punishment. But within that range could be equally lenient punishments as the second rationale.