It's one of the only fracters that can break multiple subroutines for 1, so there are a few ice where you'll get a 1 credit advantage using Cleaver rather than Paperclip. Most notably Border Control and Hagen (if you have 3 breakers in play).
With the current ice mix in play, Cleaver is a plausible alternative to Paperclip. Adjusted for ice popularity, a Cleaver costs 5% more to break the median barrier encountered than Paperclip does (ice popularity as of September 2021).* If you have Ice Carver, Cleaver costs 15% less than Paperclip to break the median barrier. There may actually be viable tournament play in this direction. (Depending on how much you value breaker efficiency vs. Paperclip's side features like not relying on combo cards, resilience against rigshooting, and being able to install on demand).
In formats where Paperclip is not available, Cleaver is currently better than Corroder. Cleaver currently costs 7% less to break the most popular barriers than Corroder does. If you have Ice Carver, a Cleaver costs 23% less than Corroder does.
*Methodology: assuming that an ice averaging 2 copies per deck will be encountered twice as often as an ice averaging 1 copy per deck. (This isn't always the case, though. Border Control tends to have a short lifespan and may not be encountered as many times as its deck count would indicate. Chiyashi can only be rezzed late and it too may not be encountered as many times as its deck count would indicate). I'm also assuming half of Hagen encounters are with 3 breakers in play.