Why would these services have to care about illegal data? The data is end-to-end encrypted, they don't know what is being sent. There is no reason to even store it on their servers.
If the service is being used to distribute malware, then they do need to care. It causes reputation issues, could get the site added to block lists, and may carry legal liability. This is why Firefox Send was shut down.
It gave you a link to be shared, that essentially embedded the cryptographic key to decrypt. It's basically the same scheme that e.g. mega.nz uses too (their "share link" feature), and similar encrypted services.
These links weren't just shared one-on-one in some private channels, but people posted the links in (semi-)public places as well. If it was something actually bad or at least "bad", a lot of times other users, law enforcement, or copyright owners would report these links back to mozilla, requesting the link be disabled and the content taken down.
