If you wanted better compression, it's called Lossless WEBP. Lossless WEBP is such a nice codec. Compared with Lossless JXL, it decompresses many times more quickly, and while JXL usually produces a smaller file, it doesn't always.
Lossless AVIF is not competitive.
However, lossless WEBP does not support indexed color images. If you need palettes, you're stuck with PNG for now.
I look forward to seeing what PNG v5 does in the future with compression, especially relative to existing formats.
How's HDR and high bit depth support? One of the things I liked about JXL is wide range of bit depths and arbitrary number of channels.