I've never seen statistics on the proportion of poetry that's subsidy published or printed and handed out by the poet, but my guess would be somewhere north of 99%. I don't mean that just for this year or since print on demand lowered costs, I mean since the invention of writing. If cavemen had known how to write, we would have been treated to a lot of poetry about mammoths and horses rather than drawings. When the great library at Alexandria burned in ancient times, I'm sure the flames were that much hotter for all of the self published poetry scrolls. A few years ago, when my local library decided to cull their collection to make room for more movies (I don't go there anymore), they pretty much tossed the whole collection of unknown poets and unread memoir. Needless to say, if you're writing with the goal of getting published, I'd avoid poetry and memoir. However, if you're writing poetry because you have something to say, self publishing or subsidy publishing is the only realistic goal for 99.98% of us.
Because the vast majority of poetry books throughout time have been self published or subsidized, only an ignoramus would think there's any shame involved. There's a reason that self publishing poetry has been so popular over the centuries - nobody was willing to pay for it. The "real" money in publishing poetry has always been in publishing dead poets Even those who had success in their lives probably earned more for their heirs after they went on to explore the great mystery. These days I'm suspicious that more money is made selling dreams of public recognition to poets than selling books of poetry. The rip-offs range from sham competitions with dubious honors as the prize to overpriced subsidy publishing deals with even more overpriced marketing that doesn't stand a poet's chance in hell of selling any books. Much of the same is true for memoir, though if you're infamous, getting published is a real possibility.
All this negativity is just the setup for my business take on self publishing poetry or memoir. It's not a business, it's not even a lottery ticket, so don't think of it that way. If you want a beautiful book you can proudly give to your family and friends, on fine paper with an embossed cover, work with your local printer and under no circumstance plan on buying more than 100 copies. You'd be surprised how hard it is to give away a hundred books, I'm speaking from experience here. If you really just want to see your poetry or memoir in print and be able to tell your ex-friends and disgusted family to buy it through Amazon or order it through their local bookstore, shop for an inexpensive subsidy press. My only warning is not to give away any rights because you never know. Prices range from free (be careful) to a few hundred dollars to get a book in print and available through distribution, I couldn't justify paying more than $500 to a subsidy publisher under any circumstance. Just comparison shop until you drop and don't get caught up in worrying about royalties because it's not a business.
The other way of getting a poem published is to sneak it into another book. The first computer book I wrote for McGraw-Hill had a poem tucked away in one of the later chapters, though I'm sure critics would have called it a limerick or a ditty. Give me a break, it's not easy to write a poem about computer hardware. The high point of my career as a poet was receiving a letter from the project editor at McGraw-Hill telling me I had to credit the poet and get a signed permission. I don't think it would be possible to hide a memoir in another book without using invisible ink, but if I do think of a way, I'll get rich selling the idea:-)