Greenmonsters
Wannabe Duck Boat Owner
If the batter/runner is already standing on 1st base when the catcher ultimately picks up the ball and throws it, how has there been any interference on the play?
The scored runner deprived the catcher from attempting a play by contacting and knocking the ball away. The catcher could have picked up the ball and thrown to first. That is a play by definition (i.e., an attempt to retire an offensive player). Whether that attempt has a high or low probability of actually achieving an out is irrelevant. You don't know what would have happened - the runner could wander off the base, the throw could sail wild out of play, or it could be unproductive as you have assumed - but as long as the ball was live there was a potential for a play.