Distros like these help troubleshoot boxes that are old/slow but also not used as computers in the traditional sense. For example network boxes, NAS, video recording boxes etc that can't run the latest LTS ubuntu well but can boot a distro like DSL. getting a vga out on these things with a fast to boot distro helps you fix things like corrupt drives, bad partitioning, bad boot loaders etc which needs a few terminal commands and a distro that boots up quickly.

It once took ubuntu 18.04 30 minutes to boot on an old dual core intel network box once. I switched to Xubuntu and it was about 5 minutes. imagine having to do multiple reboots.