Blocksize can only be increased with hardfork.
That's not true. It's proven with SegWit, which upgrade maximum block size from 1 MB to 4 million weight unit which allow block size up to 4MB. Although personally i see it's as crude approach.
Segwit has introduced a 4Mo blockhead but it only increases effective blocksize to 1.5Mo
Currently mainchain process >1500 tx/block for a max blocksize capacity of ~4000.
Quantum signatures are 50-100x heavier than ECDSA.
Signature introduction (even if hybrid or deffered) would ultimately result to 100 tx/block capacity. Well bellow current average.
Fee market will turn highly volatile and expensive. Mempool will saturate.
While this behavior seems expected, it's impact on chain stability and accessibility may turn repulsive once live.
Also signature introduction is irreversible in practice. Won't be removed during quantum era...
It's '' only trying to make Bitcoin something else as slowly, sneakily and quietly as possible.
Therefore softfork-only becomes as disruptive as a protective Hardfork would be..