IBM should not rebrand bad products as Red Hat (redwashing? hatwashing?). Maybe Red Hat could come up with a better public cloud than IBM but that would be a long-term project.
Red Hat already has a public cloud offering, it's called OpenShift Online: https://www.openshift.com/products/online/
It doesn't seem to be very successful, which is understandable since Red Hat is historically an on-premise software company, and a very successful one too. Internally they probably view Online as a sales enablement tool.
Since Openshift is already Red Hat's big bet to keep growing, presumably if they were willing and able to make OpenShift Online a major success, they would have done it by now.
Rebranding won't help, unless IBM actually put in the CapEx behind their cloud:
https://www.platformonomics.com/2018/05/follow-the-capex-sep...
I'm really surprised IBM doesn't offer a cloud product based on LinuxONE machines. These are ridiculously fast machines that are probably cheaper to build and run that the equivalent capacity in OCP x86 "boxes". And only IBM can have them.
Maybe because none of that is true? z/Architecture hasn't been (accurately) benchmarked in public for decades if ever.
Red Hat is the only subsidiary of IBM that is respected by the developer community. The rest of IBM has a very MBAsque reputation.