Is it fundamentally impossible to have a passive (NOT the expensive USB-powered active ones) thunderbolt/mini-displayport to dual-link-DVI or HDMI adapter that can support 2560x1440 external monitor?
Not only is this not impossible, but products that do this exist. DisplayPort (and therefore mini-displayport and thunderbolt) supports DVI and HDMI output over passive adapters using Dual-mode DisplayPort. Dual-mode DisplayPort only supports single-link DVI or HDMI. Single-link DVI is limited to 1900x1200, but single-link HDMI can go up to 2560x1600@60Hz with HDMI 1.3+, and bigger on new HDMI versions. In the DisplayPort 1.1 spec, VESA introduced a spec for dual-mode DisplayPort to support HDMI 1.4 output, using "Type 2" adapters.