Here's what I found out by tinkering around with settings a little.
Setting org-agenda-prefix-format to "" (as I already did before)
correctly removes the prefix *before* the TODO keyword. The
formatting
function for everything starting with the TODO keyword, however,
seems
to unconditionally insert a space between the TODO keyword and the
rest of the line. Thus, even if the TODO keyword is empty (by setting
org-agenda-todo-keyword-format to ""), there is still a space after
the now empty TODO keyword. Hence, the extra space at the beginning
of
the line. To me it seems like there's no way around this with the
standard org mode settings.