Can you explain why you feel that disqualifies it? The required input doesn't make any decisions, or hold any state as in your example; it's just "turning the crank" so to speak. Even a CPU needs a clock, right?
I'd say that a CPU that needs a clock but does not have one is not Turing-complete. CSS plus an infinite stream of user input is Turing-complete, but CSS itself is not Turing-complete. I should make it clear that I'm not saying, "my definition is the one true definition of Turing-completeness"; just that I prefer this definition. One reason I prefer this definition is that the claim "CSS is Turing-complete" makes it sound like browsers could take unbounded time to render a webpage that only used HTML and CSS, which as far as I can tell is not true.
That does seem sensible. I'll agree to a weaker, more specific claim like: HTML5 + CSS can simulate a Turing machine in Rule 110, but browsers aren't set up to do that without user input. Turing completeness level: eh.
The CPU clock is part of the CPU. That doesn't mean a CPU without a clock is Turing-complete. An ALU with access to a couple registers is not Turing-complete. "Turing-complete as long as something else provides the power to loop endlessly" is not Turing-completeness.