The problem is that RSA is also used for most certificates, including signing certificates. This attack also implicates digital signatures. While we've made good progress shifting towards DH/ECDH ciphersuites -- and TLS v1.3 will eliminate RSA entirely -- we have essentially no deployment of DSA/ECDSA certificates. It's all RSA. So "getting rid of RSA" sounds good, but won't happen in TLS/SSL anytime soon.
Moreover, if we can't get rid of export ciphersuites after twenty years, what is the probability that we'll manage to get rid of RSA in just a few? I'm not that optimistic.
There would be very little problem with RSA in TLS if people had moved to modern schemes like OAEP and RSA-PSS. The problem is that we didn't, and we're stuck with obsolete crap. Moving away from obsolete crap isn't the solution, it's the definition of the problem.
Moreover, if we can't get rid of export ciphersuites after twenty years, what is the probability that we'll manage to get rid of RSA in just a few? I'm not that optimistic.
There would be very little problem with RSA in TLS if people had moved to modern schemes like OAEP and RSA-PSS. The problem is that we didn't, and we're stuck with obsolete crap. Moving away from obsolete crap isn't the solution, it's the definition of the problem.