I'd probably skip WebP, and go straight to AVIF at this point. I believe all modern browsers support it, and it compresses better than WebP.
That is my assessment as well. The compression ratios with AVIF are ridiculous compared to older formats.
So I still end up using .jpg quite often, or .webp as a good middle ground
The default speed in libavif (-s 6 in avifenc) is fast enough, and it has been used by big CDNs to encode AVIFs for years. You can make the encoder as fast or slow as you'd like, depending on your compute/compression efficiency trade-off requirements.
Right; the issue is compatibility. But that doesn't get solved if we collectively stick to the past and only use old formats like gif and jpeg. Compatibility gets fixed by using a format, and then complaining to software developers when their software isn't compatible with our workflows. Eventually compatibility improves, and we get our cake and eat it too. Better storage and bandwidth use. And compatibility across all our software.
It just takes time.