I don't believe they were not intended for circulation, though it's quite possible they got held back. You have to look at the buildup to conversion to bronze. I've read (can't remember where) that the original date for this was to be 1858, but they ran into so many problems it got pushed back, and the sheer number of errors and dies between 1860 and 1862 reinforces that. That would explain a couple of things:
1. the huge number of overdates and varieties for 1858 as they used up dies from previous years; there is no other year in the copper series which contains anywhere near so many varieties. This makes sense if in 1857 they still intended to switch to bronze in 1858, but then decided to postpone the changeover to 1860. This would also explain the relative lack of varieties for 1859 - having made the decision to postpone, possibly late in 1857, they had time to produce dies for 1859. OR, they postponed further from 1859 to 1860 but having done so once, left themselves with enough time to create 1859 dies.
2. the low mintage of 1860 bronze pennies. (5m for a major changeover is low, especially when you look at the vastly higher mintage for 1861, 62, 63). If the problems persisted, only being resolved quite late, then they would have started striking too late in the year to achieve a high mintage. Meanwhile there may have been an emergency issue of pennies required - all they could do in the time was reuse the 1859 dies; however, if the bronze pennies then started to be struck, it may be that the limited number of copper 1860s were never needed and thus didn't get issued? Except perhaps for a few, which either got out unofficially, or a few were released before the Mint could stop them.
But what happened in the end to the small 1860 copper strike is anyone's guess. You'd have thought they would be melted down.