IMO, that's mainly because caring about coin weight (and weight in general) is a big hassle in PnP D&D. You have to manually add up all the weight of your items, changing it whenever you use or gain an item. "This treasure hoard contains 2933 cp, 953 sp, 4933 gp, and 320 pp; now we need to split that so that each character gets equal money but with weight relative to their total carrying capacity." No thanks.
In a video game, the game calculates weight automatically so it's much more reasonable to include it.
That said, I'd be perfectly fine if they removed it. Given that you can freely send items to camp, weights limits are mostly irrelevant.
