Yes, but variable-blocksize DCT is definitely used in the lossy modes (not sure about lossless).

The squeeze transform used for extra progressive decoding is effectively a modified Haar transform.

Yeah, JPEG uses the DCT, so JPEG XL needs it too to be a superset.

Yes, but if the DCT were purely vestigial, then:

1. It wouldn't have support for DCTs not in JPEG.

2. It wouldn't use the DCT in its lossy-compression of photographic content if another transform was considered significantly better.

Perhaps one could argue that they didn't want to add extra transforms, but they do use a modified Haar transform for e.g. synthetic content and alpha channels.