It's immensely more problematic. Getting out a key, inserting it into a gun, and operating it under tremendous stress (likely the most stress you've ever been

It's immensely more problematic. Getting out a key, inserting it into a gun, and operating it under tremendous stress (likely the most stress you've ever been under in your life) requires an amount of fine motor control that most people simply won't have. It'll also completely removes the element of surprise - you can't draw your gun and fire in one motion, you have to draw, fart around with a lock, then fire. Which is all the opening the bad guy needs to use his against you. I suggest taking a class, or even watching youtube videos of classes, about active self protection to understand exactly how much stress and how little time is involved in these situations.