People get so spoiled by games which allow them to fire rocket launchers while running sideways at full speed with no accuracy loss. If you tried to do something like that in the real world, you'd probably trip and discharge that bazooka into your own face.
If you wanted to shoot somebody in the head in real life, you would plant your feet and take careful aim, just like Leon does. RE4's game design choice (nothing to do with controls) to make you choose between moving and fighting increases tension by adding a slice of realism to an otherwise fantastic scenario. It forces the player to take risks and make choices between attack and escape, and reminds the player that his in-game avatar is mortal, not some god who can dual-wield shotguns while doing somersaults.
It's fun to play both the mortal and the god, but most games (especially shooters) go with the deity, so I found RE4 to be very refreshing.
"The worst part about these reviews is they are [subjective]--and their scores often depend on how drunk you got the media at a Street Fighter event." — Mona Hamilton, Capcom Senior VP of Marketing
*Image indefinitely borrowed from BrainBoxLtd without his consent.