Unexpected behavior with stacked hoppers and chests

Perhaps not a bug. I'll let you be the judge. (Sorry for the wall of text.)

The attached screenshots tell a bit of a story. The first shows the front of a simple sorting system built with chests and hoppers (in the back). Items are put into the top hopper (perhaps by water stream). Shot #2 shows that inside each chest is at least one of each item (as labeled) so only that items gets put into that chest. Shot #3 shows the back, including a fourth hopper at the bottom to catch anything that doesn't fit into the chests.

Now, the behavior I would expect goes like this: Seeds, wheat, and eggs would get into the top hopper. After a time all of the seeds would be in the top chest, all of the wheat would be in the middle chest, etc. Anything not seeds, wheat, or eggs would end up in the bottom-most hopper.

What actually happens is the top hopper tries to put seeds into the top chest, and sometimes succeeds. But, the second hopper starts pulling items out of the top hopper, so they start competing to grab items. Some seeds get into the chest as intended, but some get passed down the system with nowhere to fit and end up at the bottom hopper. The same is true for the wheat and the eggs. Shot #4 shows the contents of the bottom hopper, containing items that should be in chests higher up.