I was brought up on Ivory soap enemas by an RN mom who attended nursing school in the late 1940s. Though Mom's Merck manual listed quite a few other enema recipes, an SSE made with Ivory soap was an essential enema back in those days. Mom believed in at least one, and two were better, plain water rinse enemas after an SSE.
I agree with others that a rinse enema is not essential, but if the soapy enema was strong, for whatever reason - for effective cleaning or for "disciplinary reasons" - a rinse enema may not be a bad idea.
I like sudsy enemas. I've found baby shampoo to be very effective yet much more gentle than Ivory. Yet, if you want to get someones attention, or someone is getting yours, a very strong Ivory soap (the bar type) is the gold standard.
I've also used a variety of Dr. Bronner's soaps and while those enemas were pleasant and effective, as well as faster to prepare due to Bronner's being liquid, I don't see any advantage of Ivory of my beloved baby shampoo.
So, as mentioned by a few others, while not essential, a plain water rinse enema is still nice, especially if you simply love to take/get enemas.