Prior to 2013, US Patent 5,362,282 covered "reusable master chain link(s)":
A reusable master chain link for a derailler chain ...
Most quick-link designs haven't changed since pre-2013, when reusable master links would likely invite litigation. For example, the KMC 11-speed quick like is almost identical to a KMC 10-speed link.
Also of interest, Shimano seems to have refrained from offering quick links of any kind until after the patent expired. After 2013, though, they've offered quick links. Given the timing, I strongly suspect the patent was the real reason, despite any claims about the "superiority" of Shimano's "sooooper speshul pin". Shimano certainly abandoned that pin real fast on their top-end groupsets after the patent expired.
As noted in Weiwen Ng's answer, cyclists have been reusing quick links of all types since they've been sold, whether they're labelled as reusable or not.
Why would a company make "reusable" claims or spend money to redo existing product labels and descriptions when there's no upside? Almost nobody paid attention to the "single-use only" descriptions before, and anyone who did was pretty much ignored.
There could also be significant downside to relabeling as "reusable" a design sold as "single-use" before the patent expired. IANAL, but I can see how doing that could potentially open the door to patent infringement litigation even now. Patent holder: "Hey! We asked you about your design back in 2008 and you told us it can never be reused. Now you're selling the same design as reusable?!?!"