I like that style.
Your idea of separate bags is what I do. I have a "round the house" bag similar to yours - hammer, multi screwdriver, impact driver, screw assortment, level, peed square, different pliers, drill bits, etc.
Then task-specific bags that are add-ons to the main bag. Like an electrical bag with connectors, crimpers, strippers, meter, etc.
Harbor Freight now has a great bag for $10, with a bunch of pockets.