Lasers are an excellent training aid when working on your trigger control and follow thru. I recommend plenty of dry fire practice using a mark on the wall as an aiming point. The projected light clearly show and flaws as you pull the trigger and provides immediate feedback without firing live ammo. There's a lot more to shooting a handgun than trigger control, but you won't shoot well until you've developed the skill and a laser can get you there faster. The method you describe (looking over the sights) is fine, but I question the real benefit of a laser sight on a handgun carried for personal protection. At home I want a shotgun.
I'm a range officer at a local gun club and I've seen a number of new shooters (and some not so new) show up recently with laser equipped handguns. It's usually quite entertaining. I've sighted in a number of their guns for them (my current record is two in one day), once it became obvious they didn't have a clue how to do it. They're usually amazed how quickly I can get the laser dialed in to match the POI, but adjusting the dot to coincide with the sights isn't rocket science. Once dialed in, they wiggle the dot all over the target attempting the shot. Quite a few of them struggle to depress the button and find themselves backing off and readjusting their grip. They'd be faster if they simply used the sights or point shot looking over them. Most violent encounters are at close range (under 10') and happen quickly, where indecision and fumbling can get you killed. Depending on the color of the target, the background and the lighting, a little red dot can be tough for me to pick up, but I'm slightly color blind.
I'm a firm believer in developing basic skills first, before you start relying on technology to make your life easier. It's the same reason kids are taught math tables before they're given a calculator. If the batteries die or the unit malfunctions, you're hosed. FWIW, I like night sights for a defensive gun sights much better than lasers.