I want to do a longer answer later, but just to quickly address a few points:
1. Downloads dir is a subdirectory of the install location. You can add/remove install locations already
2. That's not a good idea. /tmp might be on a small partition, downloads might be multiple gigabytes. /tmp could also be a ramdisk, or wiped on reboot — downloads can be paused/resumed across reboots
3. v23 used to leave downloads around (to allow offline clean reinstalls, among other things), but v25 definitely cleans up after itself. What you might be seeing are just .json state files, which are a few KBs and get removed when you clear the downloads list.