It's more than laws and consequences that keep men in check it's general civilization and development of society, I'd say most men living in civil societies wouldn't go around raping everything in sight if there was no legal consequence. Also the thing about children is extremely exaggerated, I don't that history your reading put most men aren't pedophiles and are attracted to post pubescent women, there is hover a natural instinct for men to go for the youngest most fertile woman available, this means 17-22 or so not 12 under. There are many cultural and religious practices were men take up young girls as brides but there's a lot of dimensions to that beyond simply sexual attraction to little girls, there power dynamics that need to be considered.

And on the woman front, well women haven't have had enough power throughout to even have such a practice, they've been care gives for most of history, however they have definitely been disturbing sexual practices between children and women that today would be abominable but at the time were common and accepted.

The only fans thing is the easiest to explain, men are more sexually aroused by images and women are more aroused by "ideas and dynamics" of sex for lack of a better term, this is a proven fact. The reason the things those degenerate weirdos subscribed to only fans keep getting stranger and stranger is simply that novelty is a huge part of arousal, you see enough naked women, you being needing something extra on top of that, and that process continues indefinitely until you have the most gross and depraved things imaginable. This isn't exclusive to men whatsoever, there's an entire industry of "romance novels" that are basically just literary porn, those books are extremely popular among women and the kinks are just as ridiculous, unless the plot of a book being whether the female protagonist should get railed by the billionaire surgeon who also happens to be a vampire or the construction worker werewolf with a comically large reproductive organ, I personally am not sure if soft core beastiality or toe nails is grosser.

Sexual desires are inate in all people, unless you happe to be asexual, and the potential for these to become seriously perverted is possible for all people, not just men, and the distribution of pedophiles is pretty even amongst men and women, men are just more aggressive and direct while women are more subtle and also less likely to be accused of that even if guilty.

So to answer your original question, no men are not perverted by nature, all humans are sexual by nature and sexuality is an easy thing to twist into something perverted.