We weren't supposed to influence the outcome of a dropped ball previously so why should we become so actively involved now?
Well firstly, that provision has been specifically removed from the laws and no longer applies. The IFAB has made it crystal clear what is supposed to happen here. The ball is supposed to go to and remain (at least in the first instance) with the team that had possession when play was stopped.
As IFAB Circular 15 states:
The new procedure is for the dropped ball to be ‘uncontested’ – the ball will be dropped for only one player [...] Play will then continue ‘as normal’, i.e. the ball is not given back to the opponents.
The IFAB has also explained the rationale behind this and how it is done for reasons of fairness, in the explanation section of the laws:
The current dropped ball procedure often leads to a ‘manufactured’ restart which is ‘exploited’ unfairly [...] Returning the ball to the team that last played it restores what was ‘lost’ when play was stopped ...
Note the clear direction in the wording of the circular - "the ball is not given back to the opponents." If the players are not aware of this and so are doing something that is against the unequivocal intent of the law simply because they're not aware what it is, then I think it's incumbent upon the referee, as the guardian and on-field proponent of the laws, to let them know.
As I mentioned before, referees won't have to do this forever, only until enough time has passed that players have become aware of, and familiar with, the new law. I suggested this might take up to a season or so but I reckon it will probably not take even that long.
To give a similar example from a recent change, I remember a couple of seasons back when they brought in the clarification and instruction that players cannot "cut across" the corner of the penalty area at a goal kick to close down an opponent, before the ball has left the penalty area. In one of the first EPL games of the season, a forward (I think it was from Arsenal or Tottenham though I'm not 100% sure) who was obviously unaware of the new law, did exactly this - not once but twice. Now, the referee could have decided not to bother telling the player and just keep having the goal kicks retaken repeatedly or he could have done what he did do, which was to step in and explain quietly to the player what the new law said, and what he was doing wrong. I know which approach I think is preferable.