The problem is that Aurelia displays your converted HTML as a hidden tag. To get around this, simply use the RegExp function to convert to <br> , then use the innerHTML binding as follows:
<p innerHTML.bind="htmlText">${myText}</p>
This will stop Aurelia from exiting HTML. I see that you are worried about using this approach, since you are afraid that there might be bad HTML somewhere, but there is no other way around this, since you cannot tell Aurelia to show only certain tags.
If you are concerned about the possibility of bad HTML, why don't you write some custom JS to cancel all tags <br> after the page loads? (Ugly, damn it, but I see no other way.)
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