Setting default PDF preset with security options.

As already mentioned, the PDF's "Document Restrictions" are easy to override, unlike the opening password but that's not what you want.

In your case, a good solution would be a digital signature, which makes the document uneditable and unforgeable.

Because something like this should NOT be easy. 

It can't be done out of the box.

You can achieve it by custom scripting. OR you can use Output Factory (a paid product), where PDF security options can be saved with output settings and then reused automatically (disclosure: I'm the developer): https://zevrix.com/outputfactory

Even if protected there's nothing stopping them going to another vendor that removes password and prints anyway, unscrupulous but it happens. 

Have you considered share for review? Or publish online without a PDF download option?

Or using a file sharing system like Hightail, I think you can password protect files.

https://hightail.zendesk.com/hc/en-us/articles/360024661693-New-Secure-Features-for-Sharing-Files

PDF security is a good option - but if you're forgetting to add it then maybe find more secure ways to share your files. 

I don't have InDesign here to try a few things, but if there's a way maybe someone can share, as I can't try right now.

Just a few random thoughts.