PNGs will persist because I know that they're lossless by looking at the filename. When I hit File > Save as .png, I don't have to inspect output metadata (that image viewers don't expose) or play around with exporter settings.
It's unfortunate that we didn't give lossless webps a separate extension. Frankly I think even saving them as .png would've better than what we have now - people roughly understand that a .png is an image without artifacts, and any self-respecting image viewer will inspect magic bytes before opening a file anyways.
Being lossless is a function of the whole pipeline from an input image to an output image. The last step being encode to PNG doesn't guarantee anything about losslessness.
Well, you should enable Adam7 interlacing for nicer progressive decoding!
I suppose it's not very useful nowadays as most any image will load fast, though.