I didn't realize Dash uses cooked mode. That's actually kind of surprising; every other shell I've used always uses raw mode to give them more control over line editing. Is Dash just trying to be as minimalistic as possible?
Dash is really minimalistic. In its default mode, this is the only call to ioctl it makes on standard input according to strace:
ioctl(0, SNDCTL_TMR_TIMEBASE or SNDRV_TIMER_IOCTL_NEXT_DEVICE or TCGETS, {B38400 opost isig icanon echo ...}) = 0
Notice that it's merely calling TCGETS and that icanon is set, which means the "canonical input" mode with the default ^W/^U keybindings is enabled. Bash disables icanon so that it can enable line editing. Interestingly, dash seems to have vi and emacs editing modes, but they don't seem to cause dash to enter raw mode, so I'm not sure they do anything.