It is a common moral conviction that it is better to let many guilty people go free than to wrongly imprison a single innocent person. My understanding is that this principle underlies the presumption of innocence in criminal trials. I can see that this strikes us as profoundly right, but I'm not sure why. I mean, off the top of my head it seems fairly easy to refute it along a crudely utilitarian line: all we need is to suppose that the guilty parties are liable to do harm enough to outweigh the suffering of the wrongly imprisoned innocent party.

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Setting aside the question of

Setting aside the question of whether the principle 'better to let many guilty go free than to wrongly imprison a single innocent person' is the rationale for the presumption of innocence, that utilitarians would reject the principle is not as clearcut as you appear to assume. We seem to be considering two possibilities:

(a) letting some number of guilty persons (you say 'many') go free but thereby ensuring that an innocent person is not punished
(b) punishing an innocent person but ensuring that 'many' guilty persons are also punished

For utilitarians, the question of whether (a) or (b) is morally preferable will turn on empirical facts or tendencies. You suggest that utilitarians will opt for punishing the guilty even at the cost of punishing the innocent "if the guilty parties are liable to do harm enough to outweigh the suffering of the wrongly imprisoned innocent party." I suspect this move overlooks two factors that might tilt the balance of costs and benefits (happiness and unhappiness) in favor of (a):

First, punishing people has costs. Suppose that "many" here is 10 guilty persons and that punishment we're considering is incarceration. Incarcerating a person in the United States costs $14,000-60,000 per year (https://smartasset.com/mortgage/the-economics-of-the-american-prison-system). So if we follow (a), no one is punished, so the cost of incarceration (in this example) is zero. But if we follow (b), then 10 guilty persons and one innocent person is punished. That comes out to $154,000-660,000 per year. That's a lot of money in its own right, with significant opportunity cost. (How many teachers could we pay, how many roads could we repair, how many essential surgeries could we provide, etc., for that amount of money?)

Second, (b) has the difficulty that it's likely to undermine the deterrent function of punishment, which is a crucially important consideration for utilitarians when it comes to morally justifying punishment. The reason for this is that individuals will presumably come to understand that they can become liable to be punished even if they make every conscientious effort to be innocent, that is, not to commit crimes. A likely effect of (b) will be that many will commit crimes figuring that there's no particular benefit in not committing crimes, given that (under scenario (b)) there's a significant chance of being punished anyway. Put differently: If there's a decent chance of being punished regardless of whether you engage in crime or not, what reason of self-interest do you have to refrain from crime if the crime benefits you?

Again, I'm not suggesting that (a) is obviously morally preferable to (b) from a utilitarian perspective. But once we take all the likely costs and effects into account, the case for (a) being preferable to (b) looks stronger than you appear to assume.

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