True — which is one of the reasons why JPEG XL includes a risk-free JPEG recompression option: if needed, you can just undo it and get the bit-exact same JPEG files back.
Applying lossy recompression on already-lossy-compressed images is something you should avoid at all cost, since it inevitably causes generation loss (and it is also likely to not be very effective, since you're basically spending a lot of bits in the new codec on replicating compression artifacts of the old codec).
Applying lossy recompression on already-lossy-compressed images is something you should avoid at all cost, since it inevitably causes generation loss (and it is also likely to not be very effective, since you're basically spending a lot of bits in the new codec on replicating compression artifacts of the old codec).