The only thing that could possibly be effective for high speed transport is if you could put packages/mail into containers similar to the way they do on a 767. If you can load up a container and be able to load several of those into a car for high priority packages to move from A to B it could be effective. The key to high speed rail though is fast and light. The thing about freight is that it's inherently heavy...
Why do you think light in the key? It seems to me that when you're trying to overcome wind resistance, more weight equals more force that can be applied to counter wind resistance before the wheels slip. More weight does not by itself imply more wind resistance, unless the shape of the cargo changes as a result of the increased weight.
If you could run 15 trains an hour for a couple hours at night with fifty intermodal containers to the train, 80' and maybe 50,000 to 80,000 pounds per container, you'd probably have a lot more freight than can be carried by all of the planes that fly into and out of a major UPS or FedEx hub airport each day; I think the typical airplane carries about one 80' intermodal containerful of freight, and a half dozen trains might be enough to carry everything that goes through a major overnight package hub today. (Or maybe rather than have the nighttime focus, have one or two or three slots an hour for high speed freight during the day on each high speed track.)
If you can carry a lot more freight than the airlines do, larger containers than the airlines use probably do make sense.
The other question is how to prevent the freight railroads from lobbying against this, since they probably don't want to compete with government owned track that allows trains far faster than their own track. What if we had a system where every freight railroad has the option of accepting the use of HSR capacity as an alternative to accepting trackage payments for use of their tracks by Amtrak? I'm thinking of a system where for every passenger car a freight railroad allows to travel a mile on their tracks, they earn the right to run an 80,000 pound (or something) single stack intermodal container EMU for a mile on the high speed tracks. You'd need to work out some system to resolve the scheduling challenges as different freight railroads compete with each other and with passenger trains for the use of a given track.
I think if you give the overnight package companies a cheaper option than their current airplane fleet and give all the package companies equal access to that system, they probably won't be complaining; that should make more consumers willing to ship more packages, which should be good for their profitability.