I would say there is zero chance of that happening and a good chance of being refused entry totally if you attempted to use it.You need to report that other passport damaged and get the letter to enable you to get the entry's transferred to your second passport.
No idea why they stopped it at land borders but allow it at airports? They probably don't even know. It could of been when everything was being entered into the National immigration database. Land crossings were behind the airports getting it done and maybe they have never lifted the restrictions?
People travelling to there home country sometimes do it, such as the UK where we are not stamped in or out as UK citizens. A Thai for instance living in the UK will use there UK passport to leave the UK and use there Thai passport to enter Thailand. Then reverse the process when heading back to the UK. I'm not sure how it would work other than that.