It will make you in violation of the law, and that could come back to haunt you in the future, for instance when and if you want to go and visit your family back in the USA.

I would strongly recommend against going that route.

Besides that, you still have to get your 'new' country to give you citizenship as well, which will go a lot smoother if the new citizenship is paired with renouncing the USA one, you really don't want to become 'stateless' for many reasons.