Assuming you want what you've built to eventually be successful, you need to put aside that and all related fears immediately.

Indeed, that would be a short-term spiked cost. Best case scenario is your product or service page is ready, tested and optimized so it has the impact on viewers that you want. And if your bandwidth persists in being higher then that's a good problem to have.

What are the goals for your project if not getting popular/traffic/use?

The enjoyment of creating it, often my projects are small demos exploring a new method or idea I've discovered. Sharing them would be great but I don't think it's worth crashing my site or paying extra for. I'm happy to share within friends or have the odd stranger stumble across them.

"I made a thing, but I don't want it to be successful"

"I made a thing. I want it to be successful, but not that fast!"

Other problems:

1. Wordpress, phpbb, mediawiki installations will get server hacked. Databases dumped on pastebin. I think updating all software and using Docker containers may fix this problem.

2. I'll get stalked, doxed.

3. Negative comments, or even worse - it gets ignored.

If your project is popular enough to be knocked out, that's a good thing ;)

Which kind of paid hosting? Many will just suspend your account when you hit your bandwidth cap instead of making you pay more (at least, the one I'm familiar with).

AWS is a different beast, but that's what you get with the pay-on-demand model.

So...don't do it?