But what happens with e.g. a Newark – Bristol ticket where the intercity legs are roughly equal? No peak restrictions, as the journey's long enough that a late start would be too restrictive?
I would think Paddington - Bristol still because as you say a late start would be too restrictive, basically requiring an anytime.
In a new simplified fare system, individual trains would have pricing where some are slightly more than others, so some off peaks cost a bit more, some peaks cost a bit less to travel on, ending a system where a bulk of trains which are peak priced, off peak and super off peak priced.
At a machine or ticket office, a 'bundle' would be offered, so if you typed in Newark - Bristol (*note to mods, getting speculative now*) it would ask you to select the train into KX you wish to use, then suggest the connecting train at Paddington you would travel on, which you can change, at slightly increased or reduced cost. In different parts of Europe it works this way, but without you selecting a different connecting train.