The governmental theory has spent four centuries being attacked from opposite directions, and the two attacks are worth setting side by side because each assumes what the other denies.
From the Reformed side the charge is that it accomplishes nothing. If no penalty is actually borne and no debt actually discharged, then whatever happened at the cross was a display of the law's seriousness rather than a settlement of anything, and the sinner's legal position is unchanged until they respond. Critics in this line argue that the theory collapses into moral influence with a legal vocabulary bolted on, and that its objectivity is nominal.
From the other side the charge is that it is unnecessary. If God was free to relax the law, as the theory holds, then God was free to relax it without a crucifixion, and the death becomes a demonstration staged for the benefit of onlookers. On this reading the theory keeps the death while removing the reason for it.
Its defenders reply that both objections take for granted the framing the theory declines. The first assumes that only an exacted penalty counts as something real, which is exactly the premise Grotius rejected on jurisprudential grounds. The second assumes that a public act has no effect beyond instructing spectators, which is not how anyone treats public law in any other setting: a sentence that is announced and enforced does something to a legal order whether or not any particular observer is moved by it.
The theory's practical history matters to how it is assessed. It became the working account in much Wesleyan and Methodist theology, in the holiness churches descended from that stream, and in the New England theology of the Edwardsean divines, so it is not a curiosity in the literature but the position preached in a large part of Protestantism. Where a tradition holds both universal atonement and a real cost at the cross, this is usually the account that lets it hold them together.