A decent pair of gaiters absolutely can keep keep a lot of water out of your boots. The need to be a decent waterproof with a good tight fit around the ankle, a good strap under the boot and a good fit over the boot. They won’t keep water out like a wellie if you need to stand in water, but for putting a boot into a muddy hole or bog, or quickly crossing a river the no issue.
A couple of tough bin bags in your pack weigh nothing, useful if you do need to cross a river, and useful for wrapping meat when successful.
But a lot of lightweight modern boots are not waterproof. They use an inner goretex liner to keep water out. This is cheap. The boots are also made from multiple bits of leather and fabric with multiple stitch lines. This again is cheap. But each line of stitching is perfect for letting in water. A good boot will be made from just one piece of leather.
But good boots and good gaiters cost money.
Even if you have good boots, in my experience your feet still get wet if you don’t wear gaiters. Wet grass etc makes your trousers and socks wet and water runs down into your boots. Even highleg boots will allow this to happen.
Kneelength gaiters stop all water and snow from getting into your boots whilst you are walking.
I spent four hours on Saturday walking through knee length heather with lots of wet Snow. Feet went into boggy bits several times. Feet were warm and comfortable at the end of the day. Socks a little damp, but from sweat rather than external water.