I grant the Dark Emperor is disruptive, but I've heard that it's possible to send it packing by doing...something. (Either attacking the guy himself or freeing the Mii from its cage, I've heard both.) If it's relatively simple to swat him away then it may not be such a big deal.
Rainbow Road's still better than Mute City and (especially) Port Town since the individual stops have pretty good platform layouts from what I've seen and the moving platform I believe has grabbable ledges. The racers themselves are also telegraphed a good 5-10 seconds in advance by a giant flashing sign.
I have no idea how you can circle camp Tomodachi Life since every single platform is passthrough except the base.
Freeing the Mii sends the Dark Emperor away. This is confirmed by the in-game tips. It's possible that attacking it directly also sends it away, but I've never seen anything state that in-game (but of course I only have the demo).
Another thing about Find Mii is that if both players use sufficiently similar colours, you'll both get the same boosts at the same time when the stage gives stat increases.
Rainbow Road telegraphs the cars a long time in advance (an in-game tip even points out that there's a ton of warning before they show up), and of course they're nowhere near as fast nor as deadly as the ones on Mute City in Melee, so you can just see the individual cars coming and dodge them. That was doable in Brawl on Mario Circuit, so I don't see why it would be a problem here. And if you do take a hit, an extra 10%, while not ideal, certainly isn't as bad as being KO'd from 50% like the cars in Mute City did.
Also, more on Unova League and its patterns to make my earlier point more clear:
— First off, the stage transformation: The platform you fight on starts out floating far away from N's Castle in the background. When the platform flies in towards the castle, that's when the stairs snap into place from the sides. Don't stand at the ledges when the platform reaches the castle, because the stairs deal damage and knockback if they hit you on entry.
— Zekrom's attacks: I haven't watched footage of the stage in a while, but I know Zekrom roars and does a special animation before attacking, and I'm fairly sure that he has multiple roaring sounds and multiple different animations to show his different attacks. His Fusion Bolt attack has him roar and rear his head back, then cover himself in blue electricity and leave off the top of the screen. When Zekrom leaves the screen about to use Fusion Bolt, a blue glow of electricity is visible from the point at the edge of the screen that Zekrom is about to attack from. It starts subtly and grows brighter over the course of a second or two, reaching peak intensity about half a second before Zekrom suddenly zooms in from offscreen while shrouded in blue electricity, slamming into the stage. Depending on where he hits, he might knock the stage around for a moment before it goes back to normal, but this doesn't launch the fighters onstage or deal damage to them. Only being hit directly by Zekrom's Fusion Bolt attack deals damage. According to the tips section, Zekrom's Fusion Bolt can destroy the stairs, but it doesn't seem to do so reliably. While Zekrom's attacks are powerful and potentially somewhat disruptive, it's blatantly obvious which attack is coming and where, and the "disruption" only lasts an instant. On top of that, two of the possible angles for Zekrom's Fusion Bolt hit the underside of the ledges, meaning it won't hit you at all if you're on-stage at the time.
I've not yet seen footage of Reshiram's version of the stage, so I don't know anything about its attack patterns. I can only assume that they'll be just as telegraphed as Zekrom's.
Unova League's hazards can catch you by surprise your first few times playing the stage, but with a bit of practice you can learn the cues and start finding ways to use the hazards against your opponents instead.