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Many older games with female protagonists went out of their way to include random shower scenes
(hexbear.net)
(Game here is Parasite Eve 2)
It didn't happen in every game but often enough that it's noticeable. They're usually not shot as straight-up titillation, instead going for a tasteful nudity kind of thing and intended to fulfill some kind of storytelling or characterisation purpose
"You see, you gotta show them being vulnerable. They may be badass, but they're still girls, after all" 
-90s game director, probably
I'm pretty sure that 3rd Birthday is pretty much universally reviled by the fanbase and considered a personal insult
Tbh, I only played it when it released and at the time I hadn't played any of the PS1 games, I don't remember much about it. Probably killed the franchise, just like Dino Crisis 3.
There's also the fact that Parasite Eve was based on a Japanese novel of the same name that the first game is a sequel to. IIRC, Square negotiated the rights with the book's publisher, not the author whom I understand isn't interested in renewing them. That's why the PSP game isn't called Parasite Eve 3 and features a plot about time travel.
I remember reading something about Madonna wanting to make an American movie about the first game back in 1999/2000 and Square refused lol.
There actually is a Japanese Parasite Eve movie based on the book. I can only imagine how amazing Madonna's movie would've been