While you're correct that overall system cost is what matters, most functionality is offloaded to the controller because a single controller often controls multiple DRAM chips (Like the chips all share a CA bus[1]) So it's cheaper to put the functionality in the controller.

With that being said, it gets a bit nuanced, because as we make faster and faster DRAMs, we need more complicated input/output electronics (Phy and ECC.) GDDR actually has self refresh as part of the spec and even allows DRAM vendors to put a PLL inside so you can run a half rate clock, which technically makes it "Quadruple Data Rate" instead of "Double Data Rate." But usually with GDDR, you're running one controller per DRAM. Clamshell mode is not super common in my experience.

[1] I'm not super well versed on DDR4 and all of its configurations. So someone who is can elaborate if they would like.