Interesting! Given the softness of the plastic it's not surprising that some can't stand on their own... I do have some trouble with even some of the genuine ones, but the only one that REALLY can't stand ever at all is the one with no stamp.
And yeah, there were definitely bootleg ayupans back in the day... I have no idea how common they are now. But yeah, when Ayu was closer to her peak of popularity, and when bootlegged merchandise was more common, there were a bunch of fake ayupans. I couldn't tell you for sure how common they are these days, since the things that used to be used to ID the fakes - like crappy paint jobs - are things I see on ebay sometimes, but with no, like confirmation that the ayupan came from mu-mo or a concert venue, and no confirmation on whether or not they're copyright stamped. I'd need a pretty big sample size to go off of and with Ayu being more & more niche nowadays, that's something I just don't have