I think I've hit on one of the things that's been lurking in the background in my resistance to the idea of an age of accountability. Now this post will largely be assuming some things many here will not grant, e.g. exclusivism about who gets saved, Christian particularism about how they get saved, perhaps Protestant soteriology, and traditional or classical models of divine knowledge (as opposed to open theism). One reason I assume these is because I think they're all true, but it's more important for this post that most people who hold to the age of accountability as I'm about to explicate it do in fact assume all these things. Perhaps denying any of them, or at least certain ways of denying them, will get around the problems I'm about to raise. I think it might still take some work to do so, however.
The standard age-of-accountability view includes the following claims:
1. At some age (which may not be the same for everyone), each person becomes morally responsible.
2. Before that point, (a) it would be unjust for God to hold the person responsible for their sins, or (b) they aren't really sins until that point, or (c) God would always be merciful in such cases when justice might still be deserved.
3. After that point, the gospel message applies, and those who repent and follow Christ are saved, while those who don't are not.
Now there's an unspecified fourth issue that an age-of-accountability view might go either way on. What criteria determine what the age of accountability is, and do the criteria admit of vagueness such that there isn't a clear line between being morally responsible and not being morally responsible? So we get the following two views:
Suppose there is no such vagueness. Take the case of a hypothetical child Fergus. Fergus is currently below the age of accountability, and thus if he dies he'll be saved eternally. Once he hits that age, he'll magically become morally responsible overnight, even though that transition is based in capacities that admit of vagueness such as cognitive abilities, recognition of one's own sin, grasp of the concepts necessary to understand the barebones gospel message, and so on. Thus the age of accountability seems arbitrary.
What if there is vagueness, then, in how God determines whether someone is accountable? The capacities undergirding the age of accountability are matters of vague boundaries, and thus also is the age of accountability. Children become more accountable as they become more able to understand the gospel message and apply it to themselves. This means the degree of responsibility they have for their own sin and for not responding to the gospel depends on how far along they are in their moral development.
The problem with the first view is that it's arbitrary and thus seems unjust. If God draws the line of salvation at a certain point of responsibility, when one iota less would bring someone into salvation, it seems as if the consequence is far more severe than the difference in level of responsibility should warrant. With two possible outcomes of infinite difference in value, a tiny difference in how responsible someone is shouldn't be enough to put someone in one and someone of slightly greater moral awareness, say, in the other.
The problem with the second view is that it doesn't fit well with the exclusivist position that most people who believe in an age of accountability accept. I don't happen to think vagueness problems are a problem for exclusivism in general, because in my view the basis for those who are past the accountability age is still objective and clear: Is there a genuine work of divine grace in the person's life? That doesn't come in degrees. God intends salvation for someone or doesn't. God doesn't sort-of-intend things. Those with a weaker view of God's sovereignty in salvation have to say more here, but I have no problem with vagueness problems and exclusivism per se.
But once you add in the age of accountability, there is a problem, because it becomes vague whether the person is responsible for having to trust in Christ and be committed to him. Such people are on the borderline for whether they ought to be sent to hell if they haven't repented.
Now there are a couple ways someone might still hold to an age of accountability despite this problem. God could simply ensure that no one dies while in the vague area of moral responsibility where it (a) isn't clearly enough to count as a fully participating morally responsible child but also (b) not clearly small enough to count as not yet responsible. So God could avoid the unjust outcome by working it into his providential plan that no one ends up in that position.
You could instead think there are degrees of punishment and good in the afterlife. A lot of people think that anyway. But to make this work, you'd have to think the level of punishment in hell for those in the borderline of responsibility would be so close to zero that it's very near the level of good in heaven for those who are near the borderline of responsibility and end up just making it into heaven.
I wouldn't rule out the first, but the second sounds implausible given the accounts of the afterlife that you see in scripture, and even the first has to attribute to God a lot of activity that is never spoken of anywhere in Christian scripture. It brings in considerations that we're expecting God to care about that aren't countenanced anywhere in scripture. A lot of people are so resistant to the idea that infants are morally accountable for the sin nature they're born with that they might be willing to accept these sorts of things, but it's not clear at all to me that we should prefer these adjustments to the idea that there's no age of accountability and children with no capacity to reflect on their lives morally are nonetheless morally accountable to God for their sin.
Now perhaps a more helpful way to capture what I think is motivating the age of accountability idea is to recognize that what an act of divine regeneration might look like will be different for those with diminished capacities. Presumably we're not being told that John the Baptist understood the full implications of who the Messiah was to be when we're told that he leaped for joy when his pregnant mother came into the vicinity of Mary when she was pregnant with Jesus. We're being told that he was excited somehow, and perhaps a work of regeneration at that early age included an additional sensitivity even in his pre-natal state to being in the presence of divinity. Nothing I've said here tells us one way or the other about how many infants or how many of those with diminished capacities into adulthood experience something like what John the Baptist did (or at least whatever part of it was sufficient for salvation).
So it doesn't follow at all that all infants go to hell or anything like that. That's consistent with everything I've said, but it's also consistent with all this that none do, or perhaps some do. I'm not really commenting on that issue in general, just on this one approach that I think ends up with problematic elements. So I'm not sure we should try to handle this kind of problem with the idea of an age of accountability that bases moral deservingness on capacity to understand. That doesn't mean I have a clear view on the best way to approach it, though. But positive views have never been my philosophical strength.