If you're covering CAT risk 100% using reinsurers, you are at a competitive disadvantage compared to insurers who can cover some of that risk themselves...reinsurers have their own returns they look for.
That's true, but I've yet to see a primary insurer that doesn't use reinsurance.
It's not about using "reinsurance", it's about how much risk you are laying off to them. Large insurers don't insure "just the predictable losses" (unless they set up their own reinsurers) because it lowers their ROE too much to give reinsurers so much of the underlying risk.