Should we apologize to the wrongfully convicted?

Should the criminal justice system apologize to the wrongfully convicted? In a recent case in the UK (https://www.theguardian.com/law/2020/jan/13/police-reject-judges-call-to-apologise-over-wrongful-conviction?), it was discovered that a man had spent 25 years in prison for a crime he did not commit. A closer look revealed that the main cause for the wrongful conviction was the fact that police officers lied at the trial about the circumstances surrounding a confession.
The appellate court judge, now retired, announced that the police should apologize for their actions - but the police refuses to do so. Formally, the police justifies its position in that "rules were different then", so that they do not see themselves as liable for the actions in the past.
From a policy perspective, it is not fully clear whether we should demand police officers to apologize or not. The tradeoff seems straightforward: On one hand, apologizing admits wrongdoing, which may have implications for both intrinsic (e.g. pride, ago) and extrinsic reasons (e.g. fear that an apology would make the person lose reputation; fear that an apology will serve as grounds for a civil lawsuit). On the other hand, apologizing seems just and may impact the behavior of police officers and potential offenders both ex-ante and ex-post.
Starting with ex-ante, if people value apologies, these can mitigate the damage from a wrongful conviction. In this sense, this is quite similar to the economic literature's existing debate about state liability for wrongful convictions and whether or not compensation should be enforced. For instance, reducing the cost of wrongful convictions to the defendant through compensation may increase crime deterrence, by lowering the cost of innocence. A defendant who knows that he will be compensated if he is wrongfully convicted may then be less likely to opt for crime instead of innocence. The question then becomes to which degree potential criminals really value apologies. A hint can be found in an interesting experiment on Uber, run by famous economist John List and co-authors (see https://www.basilhalperin.com/papers/apologies.pdf). The researchers varied the type of apology sent to Uber users who were dissatisfied with the ride. They found that “money speaks louder than words”, i.e. only when users were also compensated, it made an impact. If this holds also for apologies to the wrongfully convicted, then without compensation apologies will no matter much.
Still focusing on ex-ante incentives, police officers who know they will be forced to apologize may be more careful, so that wrongful convictions will be prevented by avoiding wrongful arrests. On the other hand, the police may be too-careful, causing too-little arrests of the correctly identified offenders.
Ex-post, apologies per-se seem costless: why not apologize? A person sat in prison for many years for no reason – is it not morally justified to demand an apology? The problem might be in the faith of people in law enforcement: saying “I’m sorry” implies admitting a mistake, thus possibly shaking the belief that the system does not err.
I don’t have a good answer on what should be done – this should be tested empirically. But, it seems important to at least raise the question.