Do we really need lossy compression for still images any longer?
Yes. Smaller images saves bandwidth for everyone. A company like 500px from the article wants the bandwidth savings. Netflix wants AV1 for video for the same reasons, which is why they and other content providers are members of AOMedia.
Do you have any evidence AV1 is not royalty-free? These go-nowhere arguments are pointless.
VP8 and VP9 are royalty-free. Baseline JPEG is royalty-free. PNG is royalty-free. Opus is royalty-free. AV1 will be royalty-free as well.
Unless you've got something concrete to prove that AV1 can't be royalty-free, there's nothing more to say.
How can the parties participating in AOMedia be sure that no non-participating party holds essential patents that cover AV1?
How can any parties participating in any format development be sure that no non-participating party holds essential patents that cover their new format? It's a pointless argument.
AOMedia is going out of its way to avoid patent problems. That's the best anyone can ever do.
BPG is based on HEVC. The patent licensing situation around HEVC is a complete mess with three different patent pools from which you need to get three separate licenses from and some HEVC patent holders (like Technicolor) are not in any patent pool so you also need another license from them.
Fortunately, AV1 is licensed under royalty-free terms and has no such hassles.
A timeline to switch over before the first successful prototypes been demonstrated
Don't worry. They've been demonstrated.
People are always available for work in the past tense.