Where do pedophiles go if it isn't to websites that allow private messaging using fake names to under 16s dancing in belly tops?
Is that a serious question?
It seems like you're saying most pedophiles do go to this website. There are many, many ways to contact and groom children. Why do you think that this website is "pedophile heaven"? It is nothing unusual or new. Profiles can be private or locked and there can be comments or private messages. That's pretty standard for a massive number of apps.
I think you're paranoid and clueless because you are frightened by this app. You aren't alone in your paranoia and cluelessness.
I work in IT and have advised LEAs and individual IT departments in schools. Some of the more stupid concentrate on blocking access to certain websites or online services. They try whitelists, blacklists, keyword blocking, safe browsers and other methods but none work and are actually self-defeating.
You have to balance access to the internet with usefulness. You (that's any home user) could easily block access to every website except wikipedia and w3schools. It would make the internet pretty useless. You can allow access to more but it becomes more dangerous. The same goes for so many aspects of life.
Musical.ly is no different to so many apps and what does that suggest to you. Not that you should be frightened but that you should educate your child(ren) on internet safety and you should monitor their usage until they're old enough to be trusted entirely (18, IMO).
Don't teach anyone to be frightened and you shouldn't be either. Just use it sensibly as you would any other 'thing' from snapchat to alcohol.