Can a judge throw out a case where no material harm has occurred?

Question

In the Trump Hush money case, one aspect of the legal theory was that Trump violated New York state tax laws by not properly classifying the payments to Stormy Daniels when he gave money to Michael Cohen. What stands out about this is that he actually overpaid the taxes, and thus there was no financial injury to the state. But still, prosecution argues that the tax documents were indeed "materially false" that he sent to the state.

For reference, these are the instructions to the jurors (emphasis is mine):

The People’s third theory of “unlawful means” which I will define for you now is a Violation of Tax Laws.

Under New York State and New York City law, it is unlawful to knowingly supply or submit materially false or fraudulent information in connection with any tax return.

Likewise, under federal law, it is unlawful for a person to willfully make any tax return, statement, or other document that is fraudulent or false as to any material matter, or that the person does not believe to be true and correct as to every material matter. Under these federal, state, and local laws, such conduct is unlawful even if it does not result in underpayment of taxes.

Judge Merchan clearly accepted these terms, arguing basically "well, the law is the law". But could a judge throw this aspect of the case out, arguing something like "this is complete nonsense and not in line with the spirit of the law" etc. While still allowing the prosecution to move forward with the other aspects of the case (FECA violations, etc.).

Basically, what discretion does a judge have? Could this be challenged on appeal? If the country / state matters, consider this one - New York courtroom.

EDIT: Many comments are challenging whether Trump actually overpaid taxes. I will provide one more source:

In public statements, Bragg all but ignores the tax fraud theory of the case, which involves a somewhat technical violation of the law: Cohen overpaying his taxes to disguise the reason for his inflated reimbursements. Such a claim may be sustainable in a court of law, but a lack of financial harm may not resonate in the court of public opinion.

Answer 1

Many offences do not have material harm or financial injury to the state as an element of the offence (possession offences — of firearms or drugs or burglary devices, attempts, operating an aircraft without a licence, forgery, etc.). It is somewhat tautological, but offences define the wrong: they make what might otherwise be an innocuous act wrong in law.

The judge must correctly determine the elements of the offence

It is the judge's responsibility to instruct the jury on the correct law.

Even if the prosecution submits that an offence only requires them to prove elements A and B, if the judge interprets the statute to also require element C, then the judge will instruct the jury that they must acquit unless convinced beyond a reasonable doubt of element C.

Whether the judge looks to the "spirit" of the law to determine what an offence requires depends on their own approach to statutory interpretation, but for what it's worth, this is not a method of interpretation that is en vogue. Judges will generally interpret the text, informed by its context and purpose.

The judge must state the elements of the offence correctly. If the judge errs in enumerating the elements of the offence, this is a ground of appeal.

Directed verdicts

In a criminal trial, after the prosecution's case closes, it is open to the defence to move for a directed verdict of acquittal. The argument would be: even if all the prosecution's evidence is viewed through a light most favourable to the prosecution, they have failed to introduce evidence that could make out the crime.

So, if the defence believes element C must be proved, but the prosecution didn't lead any evidence of C, the defence would move for a directed verdict of acquittal.

Unconstitutionality of the offence

It is also open to a defendant to argue that the offence with which they are charged is unconstitutional, and therefore, it does not matter what the evidence is. This is another avenue for a charge being dismissed.

Civil actions: motions to strike

In civil actions, a very common early motion by the defence is to move to strike the claims.

In such a motion, everything the plaintiff has pleaded is taken to be true, and the question is whether those pleaded facts even make out a cause of action.

If there is no cause of action established even taking the plaintiff's pleaded facts as true, the case will be struck.

E.g. if the plaintiff claims trespass but fails to plead that the plaintiff had any right to the property, the claim will be struck (or the plaintiff may be given the opportunity to amend).

There is no equivalent in criminal proceedings, because there are no "pleadings" as such. But grand juries and preliminary inquiries serve a similar purpose — to provide an initial screening of a case before the trial proper.