Following on from observations about the Bat-Family, let’s look at the influence Batman has on the world around him.
First of all we have the likes of Nightwing and Batman Beyond - potential or actual legacy heroes.
Batman has more of these than average - he has trained various Robins and others to take his place when (not if) he dies, handed the role on the others, and when he went R.I.P. a few years back there were enough candidates for a Battle For The Cowl with more sides than Reign Of The Supermen before (a) the expected winner emerged and (b) the original inevitably came back.
Because the idea of Batman as a legend, the hero Gotham needs, is a powerful and interesting one. We know who Batman is, but if not for wanting to keep the original around he really could be replaced if he fell, and would be.
Ersatz superhero settings like RPGs often have built-in legacy heroes. The Superman, Batman and Captain America types are gone, and a new generation of inexperienced heroes have to take up the torch and in some cases the name. The first separately published adventure for Golden Heroes was actually called Legacy Of EAGLES and gave the PCs the chance to avenge a legendary team and inherit their base.
Would you want to create and play The New X? Might be interesting to try... either with an existing X you have to follow, or a made-up X to justify your characters.
(The closest I’ve personally come was a brief Marvel Superheroes game about a new X-Men team.)
And what other effects does he have on the setting? Some have blamed him in-character for encouraging the theatrical madmen he fights. He makes most of the Gotham police, reporters and other authorities look bad.
And he gives the people hope.
(Digression: the recent trilogy made a big point of how much more good a legend could do than one man. But as heir to the Wayne fortune, Bruce Wayne could do a lot of good. But a series about a crusading philanthropist paying for charities and encouraging urban redevelopment might not be very exciting.)
Would you feel more or less safe if you saw the Bat-Signal in the sky?