I'm tempted to switch the server over to Litespeed, especially as it now comes as a supported plugin for cPanel.

Would anyone have any objections to this?

It supports all the features of Apache, but with better performance.

None of the existing price plans would change, I'll absorb the additional licence cost.
No objection at all. I think it is great :)
How much is more performance do you get compared to using Apache?
It scales better, and works faster than apache with HTTPS. I'm still toying with the idea, so I'll keep having a think about it.