Wouldn’t the new Unbroken Bonds’ Mew ability protect the bench against those spread decks and Ultra Necrozma GX’s GX move?
Nope. Its Ability has been translated, and it appears to be the same Ability you'd find on the still Expanded-legal Mr. Mime (BW - Plasma Freeze 47/116) or Mr. Mime (XY - BREAKthrough 97/162; Generations 52/83). I don't read Japanese myself, so I'm not going through scans of the Japanese Mr. Mimes to see if they read character for character the same as Mew, but at a glance, it certainly looks like they do.
Bench Barrier's English text states:
Ability: Bench BarrierPrevent all damage done to your Benched Pokémon by attacks.
So it will stop attacks that do damage
but not the attacks that directly place damage counters or move them around. When an attack does damage, we then place damage counters on something equal to the damage that Pokémon just took
but effects that place damage counters effectively "skip" a step and are distinct. To stop those, you'll need Machoke (SM - Guardians Rising 64/145). It is also worth noting that Machoke protects against the effects of Abilities and not just attacks as well.
But spread is not the main problem. Zapdos is the main problem. And Mew does not prevent ultra necrozma (putting damage counters is actually different from an attack). Personally I've already been running sky pillar which does the same thing as mew.
I've also tried running Sky Pillar. Odds are Mew works a bit better, unless your opponent is running Alolan Muk (Sun & Moon 58/149)... but as commonly run as that Stage 1 is, more decks run their own Stadium cards, Faba, and/or Field Blower.
As for Zapdos, you may be correct.
Both matchups are pretty horrid, but I
think I have slightly more luck with the Zapdos one. Yes, that's kind of depressing. XD I'm trying to figure out if I could build a Lost March that can fit Ditto {*}, Alolan Muk, and Machoke... and get them to the field reliably enough to matter.