Since they wouldn't share the contents of their notification to their customers, we don't know how clearly those customers (router makers) were notified. But having a CVE and detection signatures would get this vuln into all the usual scanning and reporting channels, which is another route the customers might (should!) be paying attention to.
Also, I don't know how laws over there work, but there might be legal requirements to patch things once they're known, where "known" is probably defined by "has a CVE issued". So by refusing to issue one, Broadcom is blocking that process.
How is that blameless?