Yeah that's a fair point. If you don't talk to your customers today it might make sense to automate this via email.
Most likely you will have a much lower success rate since the biggest point of conversion in the approach outlined in the post is at the "2nd ask" (which is hard to do via email).
But it's a lot better than not asking for referrals in the first place :)
Would love to hear what kind of results you would see doing this!