I liked having the mail slot, but it would not go with the new front door that I have. Now I have a mailbox on the front porch beside the front door. I never noticed any air or wind coming in the mail slot, but we did not get a lot of wind, and the house was a bit leaky anyway. After that, he stopped slashing my plants. I also once caught him taking out a knife and slashing the Bird of Paradise plants along my sidewalk (He obviously did not like any leaves brushing against him), and so I reported this to his supervisor, who told me he would have a talk with him about this.
It made me wonder where some of my mail may have been going. So I had our names engraved on a brass plate (a friend who manufactures brass and bronze did this for me as a favor), and after I put it up, the postman delivered all kinds of random mail to us, regardless of the name on the address - plus mail that was for a different street with a similar name. I had a mail slot in my door in Venice (CA), and the postman told me he would not deliver our mail until we put our names on the front door above the mail slot.