Flashbacks have two uses:
one, to remind memorable scenes to TV users who might have forgotten a scene by the time it has to be remembered. After all, their situation is different than ours, who watch all episodes and sometimes binge-watch a 16-episode drama in three days or one week. Or maybe they had to skip an episode. It can easily happen that one is away from home when an episode is airing. You can't forsake all social life, for instance if friends invite you out, because you have to stay at home and not miss an episode of your drama.
Two, they are used to show us what the character is thinking/remembering, something which affects his or her decisions.
So they are very useful, when used in moderation. The problem arises when they overdo it, as you say, and especially when the remembered thing was minutes before. They could still show what the character is remembering by replaying just the crucial sentence, not the whole scene!
There was an instance when everybody was complaining, in W, of the lengthy recaps with narration. But then I read in the comments (timed and underneath) all the people saying "I am lost", "I don't understand what's going on", "Who is this guy and why does he do that?". When it was perfectly obvious for me and I didn't get lost for a second. Probably these people didn't watch carefully or skipped a crucial scene for some reason.
Some people watch dramas while doing other things, maybe going out of the room for a bit, or while doing chores like ironing etc. I sometimes watch dramas while crocheting to keep my hands busy - but I choose easy projects where I don't have to look much on the work.
While this works well with many dramas, there are some dramas which require your full attention if you want to understand what's going on, and if you want to avoid asking stupid questions. "W" was one of them. "Hwayugi" was another one.
For these people who don't pay attention, recaps and flashbacks are a lifesaver. It's a bit unfair, though, for all the rest of us, who were faithfully watching all the time and don't need them.
I have spotted a third use of flashbacks in k-drama. As most dramas are shot live on the week of release, when it's a holiday and the actors need some time to enjoy rest and celebrate with their families, there is a filler episode with lots of flashbacks. This is understandable, they need their rest, but.... Then, why didn't they start the shooting a couple of weeks earlier, to be more episodes ahead of release. After all holidays are in set dates, they don't happen as a surprise, everyone knows they will be there. Plan ahead, people! In my opinion, they should pre-produce at least half of the drama before starting.