Square is perfectly fine for any volume you want. 2.75% flat on every card, international, miles, points, etc. Also I don't need a statement for that. It's 2.75% * sales. Period.
I've been screwed upside down and sideways by "real merchant accounts". Sure the quoted fees are rasonably low but then there is extra for: foreign cards, cards with miles, rewards cards, cash back cards, Amex statement fee and on and on. Not to mention monthly fees, cancellation fees, minimum charge fees, batch fees, etc.
No thanks! 2.75% flat is a great deal as is 2.5% + .30 per transaction IF you don't have many small ticket orders (I don't).
The fact that they can't produce a statement (if this is true) is absurd though. Although par for the course with shopify. The last delight I got from them is their custom fulfillment method that reports "Success" when there was an obvious and detectable failure.