One of the biggest problems is lack of stability.
When urethane foam is produced it is made in large blocks. These blocks are monitored for internal temp until it reaches ambient. This can take up to 30 days. Then they are sliced on a large band saw.
If the foam is not allowed to completely react it is not stable enough to take temp changes.
We once sold a product that was foam filled honeycomb. On one batch we received it was not allowed to completely react. It was made and shipped in 1 week. It was used as a core material in some race car wings. When it was exposed to direct sun and was heated the foam expanded more resulting in very distorted wings.
I am not saying it cannot be done, (because it has) you need to be aware of the limitations of the process.