I don't think the problem lies in Serene Grace itself, rather, the use of Serene Grace.
Let's be honest, if Jirachi didn't have Serene Grace, would anyone ever use Iron Head? If Togekiss didn't have Serene Grace would it really be that good a Choice Scarfer? And of course, "lol dunsparce".
I agree, Serene Grace has its problems in that it "forces" luck, something which many people prefer to eliminate from Pokemon, yet at the same time, some would say it adds to the game, giving you an extra something to think about. I admit to abusing Serene Grace more than I should, but it is a cheap tactic.
Let's also not forget the impact it has on people's perceptions of hax. If a non-Serene Grace Pokemon (say, DPP Scizor) used Iron Head and got a flinch, you'd complain, and rightfully so. If Jirachi DIDN'T get an Iron Head flinch, the Jirachi user would get a tad annoyed. But then again it is only 60%. One must remember it's like Hypnosis. And as soon as Platinum was released, many analyses stopped recommending Hypnosis. So why do we rely on Iron Head and Serene Grace more, when the effects aren't as completely shut-down, and isn't any more reliable?
I also think a player's reaction is a vital part. If you were up against a Jirachi, and it used Iron Head, how many people would be annoyed that they got flinched and were unable to move? I'm sure quite a few people. But then, how many of those people would get the annoyance from not being able to fight back against a cheap tactic, and how many people would be annoyed that the flinches are actually working? This kinda goes back to my original point in that the problem lies in Serene Grace's use, not the ability itself. If you were to face Superachi and its Thunderbolt paralyzed you, sure you'd be miffed, but I think you'd be more likely to accept "it has Serene Grace, I suppose 20% was bound to happen." Now, with Iron Head which'll flinch 60% of the time, it's a different story.
I'm always against the idea of banning small facets (i.e. Soul Dew, single abilities, Pokemon + Move combos, Ability + Ability bans, etc.) in the game, so I am opposed to banning Serene Grace. I'd say the problem is more deep-rooted in players' conflicting ideas of hax and luck and what part they play in Pokemon.