The problem is using a binary vocabulary to describe something that should be on a spectrum. Just because I use an asynchronous medium doesn't mean that I don't expect a reply in a "reasonable" time, and "reasonableness" will depend on the situation and hopefully both parties are in some agreement.

Think of an asynchronous ajax call. It may be ok to wait 5 seconds, but not 5 days.

I find far more intrusive the phone call that could have been taken care of via email. I deal with this because a community service group I work with has a lot of elder people. They like to call. Yes, I understand it's Tuesday, and we have a meeting Friday, but I can answer you in two hours (by email). Don't interrupt me right now (by calling). But it can't wait two weeks.