Phase do fly close to the sun with copyright stuff, and needing to secure permission to stream certain games will become a necessity if they get to Hololive size, at least in some circumstances.
Writing off needing permission as strictly a Japanese thing like most people who talk about it oversimplifies the situation - a lot of vtuber streams where they're talking about unrelated topics while game footage plays in the background would be hard to defend under Fair Use. The reason game publishers don't sue in Western countries is because it's optics-poison rather than because they can't; if a developer/publisher sees dollar signs from a big corpo vtuber playing their game and files an opportunistic lawsuit it could honestly go either way.