Personally, I prefer text communication to calls (and asynchronous to synchronous) to such an extent that such a policy would just result in me not contacting people for simple things.

I know I'm probably rehashing an argument many here have had before, but consider: With text, the whole of your message is visible at once, for rereading. You can include links or files, and the recipient doesn't have to take any notes or do anything special to make this communication archived and searchable. With voice, you need to set aside a specific time to make the call, and the other person needs to drop whatever they're doing to accept it. And, unless you can find some special nook to do it, everyone around you is both subtly bothered by having to listen to you, and able to eavesdrop on your conversation.

The stated reason doesn't seem to hold up either--having one initial voice conversation won't help with any tone conveyance problems down the line. Unless it is used to convince you that the other person is indeed a person, and you shift your default assumption of what their tone might be (which is itself a worrying tribalistic bias, but separate). This, however, could backfire. What if your voice or in-person conversation with the person reveals some personal detail of theirs that makes you dislike them (such as an annoying voice, or personal style, or hygiene, or, more seriously, race or gender)? You'd then be less inclined to give them the benefit of the doubt in future text conversations.

Finally, I know I'm in the minority in this, but I don't get any extra benefit out of voice communications myself anyway. I'm oversimplifying somewhat, but I could say that all non-yelling "tone" is basically indistinguishable to me. Instead, voice communications often end up being a way for the more extroverted speaker to dominate a conversation through sheer force of will. My current boss does this all the time--his writing style is pretty scattered, but, whenever we Skype with someone, he'll rhapsodize at length about his abstract ideas about the current project before some of the other speakers are able to get anything in. I don't mean to be too harsh on him, because, one-on-one, his ideas and direction are often useful, but in these Skype conversations, it often turns out that it's the others' more focused additions that end up being the real product of the meeting, and his only contribution is some high-minded, well, tone-setting.