Today I was signing up with an ESP, and it was funny to see "Our email will arrive within 5 minutes" during their sign up process. My first thought was - "Oh, why to be so cautious?". But then an email arrived with a few minutes pause.
If ESPs can't guarantee their own delivery time for transactional email on one of top 3 mailbox providers - why do you expect them to provide you with any reasonable service level?
Received: from smtp1012.usndr.com (smtp1012.usndr.com. [184.108.40.206]) by mx.google.com with ESMTPS id q13si4359319wiv.18.2015.10.23.04.05.41 for <firstname.lastname@example.org> (version=TLSv1.2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Fri, 23 Oct 2015 04:05:42 -0700 (PDT)...Date: Fri, 23 Oct 2015 11:03:02 +0000