It's true and false. I had some Grado S60s handed down from my dad. While this would seem to support the original argument, he kept them in a box for about 20 years and I broke them after 6 months by tripping over the cord. As far as I can tell, most consumer goods just don't last that long (~10-ish years).
I've worn out 2 pairs of Grado SR60's and one pair of Sennheisers since ~1992, and I'm currently using a 5yr old pair of SR80s.
Each one of them has wound up needing the plug replaced, and in the case of the Sennheisers, the connection of the wire to the ear cup just got intermittent, even with replacing and tweaking. One set of the SR60s also has an intermittent connection in one of the wires near the split. I was pondering pulling themm apart and grafting in another cable, but the ear cups don't seem to come apart.
So, yeah, they last a while, there are some replacement parts, but at some point they're still e-waste.
On the other hand, making the shift from crappy earbuds to good headphones probably saved my hearing, and I wish I'd done it sooner.
Grados seem to suffer around their strain relief in multiple places - not just the plug, but also the earpiece. I have a set of 325s where, after the cable has failed yet again, I am wondering if it is actually worth it to repair them or just bin them - and that is after binning SR80s and SR60s over the years. Sunk cost only goes so far.
I love my Grado SR60s which are just about 20 years old now. The left post that the headphone is connected to needs replacement (I'm using tape for now), and I sent them to Grado to replace the cable ~10 years ago. Otherwise they are well worn but working perfectly. They are the longest running piece of my daily driving kit. The silver embossing on the letters is almost completely worn off in places just due to use. I love them so much.
It warms my heart to see youtube reviewers who encounter them and are shocked at how good they sound for the price.