Given that the article is about collision attacks and not preimage resistance, that was my main thought when thinking of the issue. I'll leave it to the experts to figure out what's the best for cryptographic hash functions.
[1] https://crypto.stackexchange.com/questions/9435/is-truncatin...
[2] https://crypto.stackexchange.com/questions/270/guarding-agai...
[3] https://en.wikipedia.org/wiki/Cryptographic_hash_function#Co...
Luckily TLS no longer does such things. This was a bad workaround in old versions of TLS. Which they then replaced by a "you can use secure or insecure hash functions, you choose" in TLS 1.2 (which is hard to excuse - at the time TLS 1.2 was written the weaknesses in SHA1 and MD5 were well known). In TLS 1.3 finally they did the right thing and only support secure hash functions.
Also please note that length is only one measurement of hash security. The fact that SHA1 is weak has more reasons. If it was a good hash function it would still have a security of 80 bits, which would not be a comfortable security margin, but still kinda not really broken for real. But further weaknesses reduced the attack complexity.
Likewise if you think about SHA256 this is not just the 256-bit-instead-of-160-bit-version of SHA1. It's a different function (although based on simliar constructions) without the weaknesses of SHA1.