Interesting find, but I'm sure there's no connection between a stage being 'home turf' and having an advantage on that level, which is good in my opinion. I wouldn't like it if every character would have an advantage (or disadvantage for that matter) on their home stage.
Also, I don't see the point about why bridge of eldin is disadvantageous(what a word ^_^) for link. If he gets seperated from his opponent, it isn't like he is forced to jump over the gap to get in melee range. In fact, I think link has an advantage over most opponents there by having strong ranged capacities. Plus, having a gap to fly over to perform your final smash must look plain awesome!
Furthermore there are many stages that give their series' respective character an advantage. Lylat system is great for fox, having platforms on two heights makes his blaster more functional and the higher set of platforms seems to be on perfect height for his landmaster to fire at. Also Yoshi's island is by far the best stage to perform yoshi's FS on, etc.
Whilst I'm sure there is no connection whatsoever, this thread sure got me thinking about how much stages affect a battle's outcome in brawl, especially with the inclusion of final smashes!