But people will vet a website that has the potential to change every day? Each time you visit the site the behaviour could be different. Vetting the site every time you use it would be profoundly tedious.

When you install an application you can vet the version you want to use, keep the installer so you can always reinstall the same version, and it only changes when you change it. That's much better control.

Luckily, all of the image editors I listed are well known and trustworthy. They're good tools. You're much better off learning them and making full use of their capability than using some limited web based image converter.

50/50 you have either ImageMagick or ffmpeg installed already.

Imagemagick also does it in the terminal. Chances are about as good as ffmpeg that you have it installed already

...which is, like, all of them released over the past 5 years: https://caniuse.com/webp

Ah, I didn't realize that always happened. I thought it was only if you did something that might have OS specific rendering characteristics (text-draws, etc).

Maybe having an ImageEncoder API might be worthwhile after all then https://github.com/w3c/webcodecs/issues/204.