It's definitely not 0.You should check the number of viable pokemon that have those intimidate-nerfing abilities (spoilers, it's 0)
Competitive and Defiant users are still pretty good in this gen, including Milotic and Braviary being the two big ones, respectively. Corviknight also has Mirror Armor to deflect the Intimidate back to Incineroar, and Galarian Weezing can just turn it off with Neutralizing Gas (it could actually be paired with one of the aforementioned Pokemon as a way to abuse Intimidate on the Weezing user's terms, activating Competitive/Defiant and potentially becoming very strong if they happened to use Parting Shot on that same turn).
Sirfetch'd has Scrappy, which not only lets it hit Ghost-types with its STAB, but also blocks Intimidate, which could potentially let it be a great check to Incineroar thanks to the Fighting-weakness.
Inner Focus is a double-whammy against Incineroar this gen, blocking Intimidate AND being immune to flinches. There admittedly aren't many good users of this, but I can name one: Lucario. It prefers Justified for Beat Up strats, but I can see some players utilizing Inner Focus as a means to offensively pressure Incineroar with its Fighting STAB while it is impervious to some of Incine's best traits, and letting Arcanine be the premier Beat Up recipient from now on. Once TPCI legalizes more Pokemon, other good Inner Focus mons include Crobat and Mienshao.
Lastly, Mamoswine has access to Oblivious, which is also now Intimidate-immune making Incine threatened by Mamo's Ground STAB.