I'm a novice at wood repair. However, my ex owned a woodworking business, so I've seen a lot, just not done it personally. So take my opinion with a grain of salt.
I'm not sure what the white stuff is, so I'm going to ignore that part until I have more information.
The other parts missing the veneer are repairable. According to Glenn, it takes two layers of today's veneer to be as thick as vintage veneer. There are several youtube videos on how to do it. You can buy enough veneer to repair the vacant spots and probably the white part from Rockler for $10.00 to $15.00. Besides that, you need glue, something heavy or clamps to hold the repair in place while it dries, an exacto knife and blue tape. Then you 'll have to refinish it. It will still look better than what is under it.
bkay