I do expect it to be a matter of time. Typically, you pull some image rendering library into your program, which pulls in a whole bunch of libraries that support the different image formats.
As such, it's the job of that intermediary library to support as many formats as possible. If you keep that intermediary library up-to-date, you may get support for new image formats without really doing anything.

But well, it may take more time for this to happen, for various reasons. One reason is obviously that we already have other image formats that may not be amazing, but they work everywhere, so most people continue to use those.
Another aspect that may slow adoption down, is that .webp was spear-headed by Google alone. Normally, you get other industry leaders into the boat, to make sure you cover everyone's use-cases and have somewhat of a commitment for them to integrate it. I assume that Photoshop supports .webp by now, but it probably took relatively long for that to happen, for example.