A number of Arminians object to reprobation on the grounds that if the atonement of Christ satisfied God's justice, then there's no need for God to manifest retributive justice by consigning anyone to eternal punishment. However, that argument has far-reaching implications for Arminianism:
i) The same logic would eliminate the justification for hell. Even if an Arminian switches to annihilationism, that's still punitive.
ii) The same logic would lead to pacifism/anarchy. Punishing criminals would be inconsistent with the atonement of Christ.
iii) An Arminian might try to extricate himself from these implications by denying penal substitution. In that event, he'd be critiquing Calvinism on its own terms.
However, an Arminian pays a price for that move. It will alienate other Arminians who are committed to penal substitution. In modern times, I think most evangelical Arminians subscribe to penal substitution because they are Baptists/fundamentalists for whom that's an article of faith.
There are modern-day Arminians like Joel Green and Randal Rauser who deny penal substitution. That, however, would ignite a civil war among Arminians.