The problem is that your wired headphones might break if you're not careful, but if you don't then they will work essentially forever. Your wireless headphones on the other hand will break at some point because the tiny lithium battery inside them will eventually stop holding charge. It's not a question of if but when.
As an addition to you post: my wired headphones do break, but I can solder things at maybe a .1 mm scale. With wireless headphones repairability is beyond my ability in many cases.
I am aware that most wireless headphones use built-in batteries nowadays, but strictly speaking, your argument doesn't relate to wireless headphones, but to products with non-replaceable batteries.
The Sennheiser RS180, for example, had rechargeable and replaceable batteries inside. Ironically, mine died a few months ago, but I am still not sure what the cause was.
