That's not how I would put it. Existing protocols that use full-width SHA-2 aren't inherently suspect for doing so, but new designs that use SHA-2 directly might benefit from doing so. It's worth remembering that most uses of SHA-2 in real protocols occur in MACs and PRFs, where length extension either isn't a problem or is addressed specifically.

Another way to look at it is, not needing HMAC is a feature of SHA-3.

In any case: SHA-2 --- in any of its variants --- remains strong. JP Aumasson, one of the Blake2 designers, is fond of saying that SHA-2 will probably never be broken algorithmically.