HTML parsers only allow this to stop pages breaking when developers make mistakes; see this Computerphile video. ‘Able to be parsed correctly’ is not the soul criterion for it a syntax being preferred, otherwise we would all leave our <p> elements unclosed.
Yes, it is not “incorrect” to write <br/>, but it is widely considered bad practice. For one, it makes it inconsistent with XML. Linters will often even “correct” this for you.
I personally find the official style (<br>) to be more readable, but this is a matter of personal opinion. Oh, and I used to have the same stance as you, but I also used to think that Python’s whitespace-based syntax was superior…
At the end of the day, regardless of anyone’s opinion, we should come to SOME consensus…and considering that W3C already endorses <br>, we should use this style.