This is in fact not true: an HMAC-based design from 2007, even one that used SHA-1, would remain sound today. HMAC hasn't changed in something like 20 years, and works even with MD5 (we've had since the 90s to make the migration from MD5 and I obviously don't recommend anyone continue using it).
To non-cryptographers, this idea that protocols need to be constantly ready to accept new ciphers in case there's a break in one of the old ones is a very big deal, so much so that every amateur crypto protocol design includes cipher suite negotiation as the centerpiece of the protocol. In reality, it's a minor concern. Which the exception of RC4, pretty much every TLS ciphersuite flaw has been the product of flawed joinery and not problems with underlying ciphers --- which is why the major breaches have forced us to move people not from one ciphersuite to another, but instead from SSL3 to TLS 1.0 to TLS 1.1.
For an expert design example, look at Trevor Perrin's Noise framework. An even simpler idea: simply specify a single set of coherent cryptographic constructions, and then version the whole protocol --- if there's a serious break in your protocol, you'll almost certainly have to make changes across the protocol anyways --- and upgrade the whole thing.