The split feature has always seemed an oddball, the way the sketch does not get subsumed, having to tell it to split, how it assumes you want new files when 99% of the time I don't. But it's never a real problem so why complain.
Here's an alternative (see image). Doesn't do everything split does, but it would do do most things I want. And it would come in handy if after a cut I find I really do still need that bit of geometry.