"Rich playboy/girl who is secretly a ninja/superhero" doesn't do anything for me unless you add a modifier to it. Bruce Wayne's is his parents' death and the torment he puts himself through for it. Tony Stark's is alcoholism and a god complex. Elektra didn't really have anything like that at first, so I was waiting for some more development, but then when that development came, it was that vaguely evil destiny silliness. Didn't work for me at all.
Yeah, the whole 'these people are going to take you in' thing is kinda ludicrous. In the comics she becomes an assassin to avenge her father; in the TV show she's always been evil, which is weird. Like why'd she go to college and then immediately become a criminal?
It's the problem with her origin being in Daredevil, but them having a loose goal of her having her own show - so much stuff is skipped over because they want to step on her toes. Most of her important backstory hasn't even been told yet.