Why can’t an iPad synchronize with more than one iTunes Library at a time?

Because the very concept of synchronizing precludes such a thing.

If you are synched with some thing it means it is the same, mirrored contents, and changes in the master library would be mirrored to the device when being synched.

If you sync with one library, you get all its contents on the device.

If you sync with a second one, that means you get the contents from that other library instead.