Let's do a reality check: These sites or "services" are not venues for selling art. They are peddlers of cheap mugs, t-shirts, buttons and baseball hats. Your art is incidental to their business. Whether you decide to place your latest masterpiece on the mug or a mugshot of uncle Joe, is of no relevance to them. Their mission is to sell you the dollar-store mug at a $12.95 mark-up and give you the hope that someone will buy the same and earn you a $1.50 "commission" on your work.
I admit to selling my work through Giclee reproductions. Giclees, unlike mugs, are high quality reproductions of artwork. Their purpose is to allow people who enjoy your work the pleasure of owning it at a budget price for the purpose of hanging on their walls and enjoying them as art. That is hardly what a mug or button aspire to do.
I know that I am going to be branded as an elitist-snotty-art-wannabe. I'll take that. I think there is a point at which an artist needs to examine their self-image and decide what kind of art they want to produce and for what purpose. And if you find yourself producing paintings with the mug in mind, more power to you. At least you will have made a conscious decision that this is the way you want to interact with the world... You will excuse the world then for interacting that way with you and asking for volume discounts!
.... I'll get off the soap box now.