Is there any particular reason to prefer Presto integration? From a London perspective, the Oyster fare card has largely been rendered redundant by contactless credit/debit cards and Apple Pay. (The only exceptions are certain people, such as kids and retirees, who get discounted fares, as well as certain types of season passes - but I'm sure they'll eventually integrate these one way or another).
From what I've heard, Transport for London prefers to cut down on Oyster card usage because the costs[*] of operating their own fare card system exceeds whatever fees are paid to banks to process contactless card/device transactions.
[*] producing physical cards, maintaining machines and staff to process "top-ups", paying commission to retailers who sell top-ups, increased crowding at stations while people stand in lines to top up, etc