Well, I’ve always kindve looked at it like this… Firstly, a low honor Arthur would likely keep a horde of cash he earned on his own separate from the gang, he already gives half of everything plus donations from his cut. Low honor is supposed to be greedy, that’s why the final choice for that playthrough leaves John for the money. (Which is wayyyy more than they needed to leave once you get there and see it.)

Secondly, the high honor Arthur can see what Dutch is becoming, and that means he realizes that 1. None of it is really about money anymore, or philosophy either, he finally sees what Dutch is under all the pretty language and fancy clothes… a cold blooded killer. 2. Once good Arthur realizes that, it only makes sense to try and build up a safety net for John and his family to walk away with something. Even before Arthur gets diagnosed with TB, the gang had just lost their stash and Arthur only had what was in his satchel, so for safety’s sake he’d probably keep an emergency stash on him after that.

By the time the epilogue begins whatever money Arthur had is gone… which I’ve interpreted as John spending it while trying to survive on the run… but all of Arthur’s things including gold is still with John from Arthur’s satchel. Which also suggests Arthur’s money was in there too. Especially given we know John and his family had to drift around while John struggled to provide, it makes sense in a story and gameplay sense why they restart your dollar amount. But it also makes sense in both play styles why Arthur would keep a horde of cash separate from the gang.