Why cPanel doesn't support LiteSpeed is a complicated question. Perhaps the biggest reason is that most people in cPanel are experts in Apache, but not experts in LiteSpeed. They recognize that Apache and LSWS are similar in some ways (which is why they are willing to look at LSWS installations to some degree now), but they are reluctant to go so far as supporting it unconditionally. That would be a big, time-consuming step for them.
We have talked to them about this in the past and are still talking to them. Recently, they have shown more interest in LiteSpeed, though they are still far short of ready to make the jump to supporting us. I think we're on that path, though, and that it will happen in the future.
Please let them know what you want. They know that there are many LiteSpeed users that use cPanel, but it will help to show them just how many people want this.
"...of shoes and ships and ceiling wax/ and cabbages and kings,/ of why the sea is boiling hot/ and whether pigs have wings."