that's what I was wondering, too. How is it incompatible? Wrong gauges?

It's combination of tunnel ceiling height, weight limit, and chassis mounting compatibility. I'm not completely sure there were protectionism of either directions are involved with JNR/JR 12/20/31ft system and ISO 20/40ft, both seem to have been conceived around the same time in mid 60s.

JR (on which freight trains do run) network is 3/4 gauge, but JR shinkansen and other operators use standard.

>but JR shinkansen and other operators use standard.

That's irrelevant. The shinkansen tracks cannot be used for cargo trains: they're exclusively for high-speed passenger trains.

You can't share tracks between slow cargo trains and high-speed passenger trains. Not only is the scheduling impossible, but the cargo trains would ruin the tracks. The shinkansen tracks require frequent and thorough maintenance to keep them at the level needed for reliable high-speed service.

If you want to see what happens when you try to share tracks between cargo and passengers, just take a look at Amtrak. It's a complete disaster.