In business contexts[0], you don't have to choose between being impolite to some people and annoying others. There's a solution that satisfies everyone: just follow your pleasantry with the thing you really wanted to say. Do it immediately. Start typing your request immediately after sending "Hi $name", so that the other side sees the typing indicator. Or better yet, use the magic of Shift+Enter, supported by most IMs out there. Send a single message containing a bunch of pleasantries, followed by a newline (Shift+Enter), followed by the real payload.
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[0] - This is slightly different in personal space. When a long-forgotten acquaintance reaches out to me, I already know they want something, and I wouldn't be offended if they skipped the useless pleasantries - but apparently enough people demand to be taken through the "how are you and your kids?" dance first, that it's unsafe to state the actual purpose up front. But in business conversation, you're not supposed to go deeply personal like this, so there's no ambiguity - the reason for communication is business-related, by definition.