Companies do this via E-Mail? Where I work you send someone a Google Calendar invite and they click "yes" or "no", and they can see if you have a free spot in your schedule beforehand, so it rarely goes wrong.
Sure, but the transport part isn't relevant to what the GP is mentioning, which is that apparently Japanese etiquette requires you to write some amazingly long E-Mail. With a calendar invite all that's abstracted away and you just get "can you make it at such-and-such date at such-and-such time? yes/no/maybe".