Publishing with KDP and IngramSpark is possible, as long as you don't sign up for Kindle Select. My last three books, I published through both KDP and IngramSpark at the same time. (Use these links to get started – there are phonies out there!)
Why both? There are a few other legitimate companies, but KDP is the least expensive I’ve found. But many bookstores and libraries prefer dealing with Ingram, which is where they purchase most traditionally published books - IngramSpark is their platform for small indies.
I did expanded distribution with KDP, so my books are available widely (including Nook). While my royalty is higher when sales are made directly at Amazon, some people do not shop there! I still get a royalty when a book sells elsewhere.
I’m not sure I’ll do IngramSpark again. They charge each time you upload a manuscript, and their process is not user-friendly. Just getting sales reports is complicated. I’ve been spoiled by Amazon’s efficiency and most of my sales are still through Amazon.
Also, I may try signing up for Kindle Select when I launch my next book. "Boosting" blog posts through my Facebook page is increasing traffic at this website, so getting a boost from Amazon may be a good way to increase sales on a new book. If I do participate in Kindle Select, eBooks can only be published/sold through KDP. I'm not sure it would be worth the hassle to sign up for print-only at Ingram.
One more thought: Another reason I like KDP is not currently true.
When we did a school yearbook with them, we never hit publish. The school was able to buy author copies (not labeled PROOF), then sell them to parents. This avoided concerns about the kids’ photos going out onto the web. It was also nice for people who wanted reasonably priced books just for family.
Amazon eliminated this option – so it’s not currently available. They’ve had complaints and are reconsidering. I’ll let you know when they go back to it.