See, you're mostly wrong. Cali Franchise Tax board ONLY taxes TAXPAYERS. And taxpayers are defined by the IRS as US citizens and residents. Therefore Non-resident aliens are NOT TAXPAYERS. Furthermore, the Cali FTB gets the taxpayer info from the IRS. So if you're not a US taxpayer on federal level, you aren't one on the State level.
On top of that ALL gov't agencies operate within the FEDERAL ZONE. And that requires having an address with a ZIP code. And they didn't make that ZIP code up; YOU GAVE IT TO THEM, since they would NOT deal with you if you told them that you have an address without ZIP code.
Addresses without ZIP codes are FOREIGN to their federal zone! If you don't believe it, just try to get a driver license by insisting that you DON'T live in a ZIP code. IT CAN"T BE DONE!

See, the current governments ALL operate in the FEDERAL ZONE and that REQUIRES having a ZIP code address. No ZIP code address = no gov't jurisdiction. Etc. etc.