My idea of the day is to award a set amount of prestige point for a Cradle and All run. It wouldn't be a "once per day" thing rather a "once per gate" thing. So you couldn't get the prestige by doing it multiple times on the same gate. You can do it on all four active gates, but if you have done all four, you would have to wait until a new gate cycled in before doing it again for prestige.
Or perhaps you could do it several times per gate with a set amount of times. Prestige would be less and less each time.
Not sure how feasible this will be once the Arcade Redux is fully established since we don't have a lot of insight on the changes that will occur.
Not sure if this would be compatible as 'apparently' prestige missions have story lines. It wouldn't make as much sense lore-wise.
BLOOP
Interesting idea though.