Currently, the president is obligated to find a nominee that the Senate is interested in having as a justice.
Those are serious constraints on his power: he can't legally NOT act, and his actions must reflect the preference of the Senate, even if those aren't his own.
Your proposal turns that on its head, allowing the president much more latitude to nominate the person he personally wants even without review from Congress AND it gives him a way to intrude into Legislative Branch business, prompting the Senate to interrupt its other work to take up this issue.
Imagine, for example, if the Senate is working on legislation the president doesn't like. He could start sending over nominees that he knows they'd find unacceptable, just to have them stop work on that legislation to debate his nominees endlessly.
So yeah, an awful lot of power for the president to exercise unilaterally.
