The point should be "don't use a bad carousel" then. It frustrated me that it didn't paused when my mouse was over the slide and that the timing was badly done (on purpose, I guess).
I've used them and my clients and the customers of those clients were happy with them. I did not through paragraphs of text on them, just pretty images and headlines (featured content).
> "It frustrated me that it didn't paused when my mouse was over the slide"
Even if you did this, your mobile users will still be mad, because they cannot hover.
The question isn't if you or your clients are happy with them. The question is if your users are happy with them, and if they generate better business results (conversion, clickthrough, whatever is relevant to you) than the simpler, less Javascripty, less timing-based, less gotcha-with-the-mouse-hover implementation.
Though some have a habit of stubbornly ignoring any professional advice against a feature they have an emotional attachment to, raw data can sometimes snap them out of it.
I am a mobile user, and I can hover. In Chrome on Android, when I tap on an element that doesn’t have an action of its own, that element always acts like the cursor is hovered there. I was able to use this to pause the carousel on http://shouldiuseacarousel.com/. And on other sites, if I tap and hold on a link, then close the dialog that pops up, the link still acts like it is hovered over.
Text in a carousel is a no-go; pausing when hovering is a neat idea, but not possible on touch screens, nor easily discoverable by the average user. Even if the timing is long enough, I still feel stressed out by the fact that I know the text could be dragged out of my sight any time, which stresses me out so much that I can't concentrate at all on the content.
The second terrible mistake is using page indicator dots (which do a good job of indicating the page) for navigation, let alone using them as the only means of navigation!
When you take into account these two things, a carousel can actually become comfortable to use and may no longer enrage its users. But that's still a far cry from being better than showing the content in a regular list:
> I've used them and my clients and the customers of those clients were happy with them.
What do you mean with "happy"? Did the customers actually understand how to use the carousel, did they discover its content, did they click on it? Not being annoying does not suffice to qualify as useful.
I use adblock to eliminate all elements on the page that animate. I can't read blocks of text with animation running in the corner of my eye - it's too distracting. I run flashblock for similar reasons.
Happens most often on newspaper and magazine websites. Some sites provide a pause button to kill the distraction, but many don't.
I've used them and my clients and the customers of those clients were happy with them. I did not through paragraphs of text on them, just pretty images and headlines (featured content).