Thinness likely has little to do with the issue. Turns the middle where the HDDs are there was no huge thinness reduction. More likely it is cheaper for Apple to share 2.5" drives with the Mac mini. More drives bought in higher number. Shared components across the Mac line up is standard Apple practice.
It is also a bit simpler to do the fan as they did.
Comparing the two insides the 21.5 model mounts the HDD horizontally.
Image
[ from iFixit teardown
http://www.ifixit.com/Teardown/iMac+Intel+21.5-Inch+EMC+2544+Teardown/11936/1 ]
versus the 27" model vertically.
Image
[ another 27" found on the web.
http://www.mactrast.com/2012/12/first-27-inch-imac-teardown-hits-the-web-beautiful-inside-and-out/ ]
If the 21.5 model moved the fan out of the way (higher ) along with some tweaks to the speaker/air channel assembly they probably could slide a 3.5" drive in there. It would drive up Mini costs and 21.5 costs but they could do it. I'm sure they'd pass along the cost increase too.
As storage densities increase those the 27" will likely pick up 2.5" drives ( further broadening the parts commonality) rather than trying to push 3.5" into the 21.5" with a tweaked design. Folks are right Fusion over time largely address performance issues. Natural HDD evolution will address capacity. Price and capacity are the only dimensions HDDs can win at against SSDs. They have to get better or disappear.