Write function in one line into ~/.bashrc

There is a ; needed at the end of the function:

list(){ ls -a ; }

should work.

The syntax of a function definition for bash is specified as

name () { list ; }

Note that it includes a ; that is not part of the list.

That the ; is required in this place is kind of a syntax anomaly. It is not bash specific, it's the same for ksh, but it the ; is not required in zsh.

Functions in bash are essentially named compound commands (or code blocks). From man bash:

Compound Commands
   A compound command is one of the following:
   ...
   { list; }
          list  is simply executed in the current shell environment.  list
          must be terminated with a newline or semicolon.  This  is  known
          as  a  group  command. 

...
Shell Function Definitions
   A shell function is an object that is called like a simple command  and
   executes  a  compound  command with a new set of positional parameters.
   ... [C]ommand is usually a list of commands between { and },  but
   may  be  any command listed under Compound Commands above.

There's no reason given, it's just the syntax.

Since the list in the one-line function given isn't terminated with a newline or a ;, bash complains.

The end of a single command (";") is implied by the newline. In the oneline version } is parsed as an argument to the unterminated ls -a command. Which you can see if you do:

$ foo(){ echo "a" }
}
$ foo
a }

See how the command inside the function declaration swallows the trailing curly brace?