If the additional area is used for new hobbies, hosting guests, or something fulfilling and interesting, then sure it can help keep the mind active. But people don't usually retire so they have more time for vacuuming or dusting. Many elderly people simply don't have the energy or interest to maintain their homes, it slowly falls into disrepair.

Heavy confounding there. If they’re declined enough to not drive, they’re declined in a ton of other ADLs too