Is it permissible to burn everything on which Arabic letters are written—even if it does not include any of the Beautiful Names of Allah, or Quranic verses, or the names of the Prophet, peace be upon him—to avoid their desecration by being trampled upon or thrown into waste bins?

Some scholars have deemed Arabic letters impermissible, but the more correct view is that the prohibition relates to what is written that is sacrosanct in Islamic law, such as the name of Allah or the Quran. The mere names of prophets do not warrant veneration; thus, the name Muhammad or Isa does not necessitate reverence. There is no evidence for the obligation to respect a mere name or letters. Your friend should abandon this act as it causes him hardship and difficulty, and it may lead him to obsessive thoughts (waswasa).