It's not a blocked ball.
USA Rule 1-Blocked Ball: A batted, pitched or thrown ball that is stopped, touched, or handled by a person not engwg d in the game, or which touches loose equipment or any object that is not part of the official equipment or official playing area. NFHS has same definition under rule 2-2-3.
Clearly the batter is "engaged in th game".
Absolutely correct, it does not meet the definition of a blocked ball. I used the term out of laziness and efficiency in explanation.
In a perfect world, the umpire would have noticed the catcher was having difficulty getting the ball, checked to see if there was any action on the basepaths and call time when it was discovered no runners were attempting to advance.
I certainly don't want to call time every time a pitch is on the ground near the batters feet.
Fair enough on using term blocked ball. But I don't even like to call time when a defender is holding a tag on a runner for extended period of time hoping the runner will get off the bag. I certainly don't want to call time every time a pitch is on the ground near the batters feet. I think the batter has a modicum of responsibility to step away from the ball and allow F2 to get it without kicking it away from F2. If the batter cannot do this and the runners advance because of the kicked ball and F2 is hindered from making a play by the act of the batter kicking the ball away you have all the elements of interference on the batter.
In a perfect world the offense would notice that their batter had just kicked a live ball away from the defense and would have their runners stay put. If there is no play for the defense to make there is no interference.
Ok.. the batter contacts a live ball.. in this instance kicks it away from F2. What rules allows me to kill that play besides the interference rule?
A pitch that strikes the batter or her clothing would do it but this was a pitch that came to rest in the box and did not hit her. Then she kicked it. So it's not dead on HBP.
Let me ask this.. assume a totally different play with a similar ending:
Runner at 1B. Batter hits fair ball to outfield throw goes home holding runners at 3B and 1B. F2 return throw is not caught by F1 and ball rolls to feet of runner standing on 2B. Runner at 3B stays put. Runner on 2B kicks ball away from F4 ho is trying to retrieve it and then the runner st 3B scampers home.
Is the runner st 2B scott free because the runner at 3B was not running for home at the time the ball was kicked away? Would we simply call a dead ball and put the runner back on 3B? I think not.
In either case (the OP play and the play I describe) there is no need to judge intent just the fact that an act by the offensive player hindered the defense from making a play. I don't see that it matters when the advancing runner started advancing just that the defense was hindered from making a play due to the act of an offensive player.