Our Joker (Joker Prime?) doesn't care about devotion and allegiance though. He's certainly quite good at accumulating it when he wants to, but it's all a means to an end, and he works just fine alone or manipulating people from the shadows too. As mentioned, I don't get that vibe from Arthur at all, nor do I get much in the way of organized crime (even the very loose version of "organized" the Joker typically uses). But most of all I'm just not seeing the age difference; sure, the comics have always been vague on that front, but 3 decades+ are a bit much.
Batman as a film franchise doesn't really help your point though; none of his movies ran concurrently, or even all that close together. The Tim Burton -> Schumacher era was 4 movies long, each one 3 years apart between installments with nothing in between - no teamups, no spinoffs, no crossovers etc - from 1989-1997, and were only loosely connected to one another at best. This was followed by an almost ten-year gap to the Dark Knight Trilogy. With Batman movies spaced out that much both within and between their respective runs, of course there was no confusion about them being largely (or completely in Nolan's case) unconnected to one another.
Compare to Marvel - the MCU would have never gotten off the ground if they tried multiple versions of the same character. For example, in the same span of time as the first set of Batman movies, RDJ played Iron Man in more than twice as many films, was assumed to be off in the background somewhere doing stuff for several more, and even when he had nothing to do with the plot, setting details from his movies were sprinkled throughout several others and in multiple spinoff TV shows. Even posthumously he drove the plot of Far From Home. Could you imagine trying to keep all that straight if there were multiple Tony Starks running around with so little space between? It would be utterly impossible, and so it's perfectly reasonable that they didn't try.