How would presidential line item veto help resolve the issue of earmarks?

In the United States, at least, a line-item veto for the
president has been found unconstitutional.  This means that such a veto would not be
able to help resolve this issue without a constitutional amendment allowing it (or
without the Supreme Court reconsidering).

If it were legal,
a line-item veto would resolve the issue because it would allow the president to remove
specific earmarks that were not economically useful.  In Congress, such earmarks are
used to "buy" the votes of specific members of Congress.  Congressional budget writers
have a hard time refusing to give earmarks because they might need a favor some day from
the person requesting the earmark.  Therefore, they give out earmarks to create
political support for themselves.

In theory, the president
would not need to do this.  He (or someday she) would be able to veto unnecessary
earmarks because he would not need to work closely with particular members of Congress
in the future.  This would allow the president to cut the budget in ways that Congress
is unwilling to do.