First, about Mac:just because i'm interested - what biases does battlefield have? the only real bias i can think of is little mac getting platform camped to death, but that's true on every non-fd stage. rosalina exploits the platform layout pretty hard, but then again rosalina exploits all platform layouts. characters with vertical combos like the platform heights, but a bias towards vertical combos is built into the game (vectoring and worse vertical di), and the higher ceiling somewhat compensates for it.
not disagreeing, just interested to hear what you think they are
Town & City is great for Mac, maybe better than FD. The platforms disappear at transitions, so camping him indefinitely is not a viable option for most characters. And Mac kills predominantly vertically, so low ceiling == great.
Mac can full hop onto/between platforms on Battlefield, and many other stages. Battlefield is not actually that bad for him, though obviously not his favorite.
Mac cannot full hop onto Smashville's platform in Smash 4. Combined with its off-stage behavior, Mac can do very little to an enemy on the platform. On Duck Hunt and Smashville in many matchups, MAc basically loses if he ever falls behind. In some matchups, Duck Hunt might actually be preferred, because a losing character might have more ability to harass Mac from the platform anyway than to do so from the tree.
Mac does decent on many of the other stages that are no longer legal, including all traveling stages and Castle Siege. He'd prefer most of these to Battlefield in most matchups.
On the modern list of 5, Mac should be striking to Lylat against any opponent smart enough to strike FD and T&C. He should always ban Smashville and be CP'd to Battlefield.
Battlefield is just the most skewed of the "nuetral" stages for vertical strings, as you described. However, the narrowness makes escaping to the ledge/offstage more accessible, and the platforms are at least narrow enough to allow some interesting counterplay. (Contrast with the extreme case of Tomadachi Life)