The omission of the preposition 'to' is optional here. ) Are you at home now? / Are you home now?
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I think you are correct. Stated alone "I wrote him" implies that the speaker wrote the word him. "I wrote to him" implies that the speaker sent a message to someone. So not including "to" leads to ambiguity if stated alone and thus potentially, ambiguity in any context, representing poor communication/ use of language.
"I wrote him" is absolutely incorrect. "I write" (without "to") requires the question "What" but not "to whom" " I am not a letter you to "write me" : ) Even Grammarly tries to correct it while I am writing!