Even if the above were just an individual... bafflement? and not an actual issue, the size savings really don't seem worth the compatibility hassle, the extra manpower/workflow complexity to support 2 formats, the additional storage (and caching) caused by this duplication.
And the above is if it's done RIGHT. 80% of people outside this forum won't understand that you're not supposed to convert from a lossy format to another, and just convert jpegs to webp.
Webp seems so pointless. A progressive jpeg with an optimized Huffman table can be understood by a 27 year old decoder without issues, achieves 90% of the quality/size claims of webp and can be produced losslessly from your source jpegs. This is without even touching Arithmetic Coding (also lossless, part of the official standard, but poorly supported due to some software patents, even though they all expired by now), or playing with customized DCT quantization matrices to get more compressible outputs (incurs a generation loss, but produces standard files).