You can't do display none for BR element.
But even if you could, you wouldn't want to overwrite it for the entire website. Also, the HR element is a very old, largely unused, and styleable, so its a good candidate for this.
Sure, you don't want to override it for the entire web site, but if you're being specific enough about showing/hiding line breaks at certain breakpoints, then I don't see why you can't just specify with the class of the container (or whatever) which particular BR you want to hide in a given context.
:D
<strong>Headline</strong><br> The quick brown fox jumped<hr> over the lazy dog.
And the code is clear and easy to read.