Sabin, however, is literally the brother of another cast member who lives in the mountains.
Except that their father was murdered by the Empire. Pretty important motivating factor.

Locke, for example:
He wants to protect Aeris because he was unable to protect Rachel. Later, he finds the Phoenix materia but is unable to revive her.
He wants to protect Dagger because he was unable to protect Rachel. Later, he finds the phoenix pinion but is unable to revive her.
He wants to protect Yuna because he was unable to protect Rachel. Later, he finds the phoenix fayth but is unable to revive her.
Red XIII:
He bears a grudge against the Empire because it ran experiments on him.
He bears a grudge against Garland and Kuja because he was an experiment of the Terrans.

As I said, this complaint could be made against nearly any character in nearly any entry in the series.

It's a thread about the quality of VI versus how people perceive it. Saying that a problem isn't a problem because it's a common problem doesn't actually support any suggestion that its not a problem. Compare to support, don't compare to show how something else is wrong, too.
As I've said, your assertion that a story is weakened because the characters are not inextricably linked is not supported by anything other than "because I say it is". This is pretty much a necessary feature of all but the most tightly knit ensemble casts, and it's not the sort of thing you get in a video game.

Games having more than an excuse plot is an entirely recent trend. Does Mario need a reason to jump on all these platforms? Let's just say he has to rescue the princess.
No, but FFII and FFIV certainly had a lot more than excuse plots, so FFV having an excuse plot is a bit of a step backwards.