What would the downsides be for allowing that to be clicked? I can't really imagine that there are any, and it'd definitely help with consistency if this input icon component served a functional purpose when it's used (similar to the one on the password field and number input). There isn't really any sort of indication of whether or not the icon is functional or decorative, especially on mobile when there is no hover state
There's no significant downsides to implementing it, nor are there particularly significant upsides. I'd rather we spend our time adding stability and functionality to the software rather than making superficial changes. Especially when those changes are essentially suggestions, and not actual bugs.
I completely agree with Jake on this. I often click the icon first as that seams to be the logical place to click if you want to bring up the calendar. I suspect many XenForo users also do the same. Please make the icon a link.