Why indeed? Wouldn\'t something like &br; be more appropriate?
A tag and a character entity reference exist for different reasons - character entities are stand-ins for certain characters (sometimes required as escape sequences - for example & for an ampersand &), tags are there for structure.
The reason the tag exists is that HTML collapses whitespace. There needs to be a way to specify a hard line break - a place that has to have a line break. This is the function of the tag.
There is no single character that has this meaning, though U+2028 LINE SEPARATOR has similar meaning, and even if it were to be used it would not help as it is considered to be whitespace and HTML would collapse it.
See the answers from @John Kugelman and @John Hanna for more detail on this aspect.
Not entirely related, there is another reason why a &br; character entity reference does not exist: a line break is defined in such a way that it could have more than one character, see the HTML 4 spec:
A line break is defined to be a carriage return (
), a line feed (), or a carriage return/line feed pair.
Character entities are single character escapes, so cannot represent this, again in the HTML 4 spec:
A character entity reference is an SGML construct that references a character of the document character set.
You will see that all the defined character entities map to a single character. A line break/new line cannot be cleanly mapped this way, thus an entity is required instead of a character entity reference.
This is why a line break cannot be represented by a character entity reference.
Regardless, it not not needed as simply using the Enter key inserts a line break.