I generally enjoy the content that Trail of Bits puts out, but the harsh tone and use of explatives seems only for the sake of attention to a non-issue. RSA, the algorithm, is generally safe for real-world use. It is possible to use RSA securely (we've been doing it). However, there is indeed an issue.

Lets define the issue: Poor understanding of cryptography leads to poor implementation in practice.

This issue applies to any crypto algorthim, not just RSA and ECC. If everyone dropped RSA tomorrow in favor of ECC, would all of our problems be solved? No.

How to solve this issue?

1. Increase understanding of general cryptography. It is a dense subject.

2. Make implementation of cryptography easier. This is slightly more difficult though, as it depends on your use-case.