If these paths were available to run, why would they be better as an OAO than with GTR?
Because if they where an OAO, they would be just concentrated on those routes and would make sure that replacements for those journeys are in place if the paths cannot be used. Whereas GTR are sometimes not making sure that there is any replacement transport when engineering works take place for example. It is a case that oh well, just use the local Brighton & Hove bus service as we cannot provide replacement bus service to get you to Lewes to change trains to get to London. So, you end up taking the 12, 12A or 12X service into Brighton and then travelling up from there instead. That having been said, it is cheaper to do that in travelling up to London. With an OAO also offering an alternative service, it would hopefully bring the prices down so that maybe more people travel on the train into Brighton rather than the Bus.
Even if an all day every 25 minute service was possible without getting in the way of anything else, it is debatable whether that would actually be better than a regular 2tph leaving at the same times each hour.
But that is the thing, you look at the timetable of the trains, it is not the same times through the hour, all the way through the day. The trains start at 4:50am, the next train is at 5:25am, the next 30 minutes later at 5:55am, the next 30 minutes later at 6:25am, the next 25 minutes later at 6:50am, the next at 7:23am, the next 30 minutes later at 7:53am, this carries on for the trains through up to 8:53am. The next train then is 32 minutes later at 9:25am, then at 9:53am which continues at this times through the hour until 12:25pm. Then you have to wait an hour for the train at 1:25pm. Then the trains return to 53 minutes past the hour and then 25 minutes past the next hour right through to 2353 service.
Now, since I grew up through the 1970's/1980's the areas through from Brighton to Eastbourne have become more areas where people that work in London commute from to get to work. Even after Covid, it is possible to see people travelling two to three times a week up to London. The journeys for those in Brighton, Lewes or Eastbourne areas is simple, just walk on a train then to travel up to London. For places like Seaford, which previously did have a train up to London each day and back in the late afternoon/early evening, you have to change at either Lewes on to a crowded 4 car or 8 car train or travel on to Brighton to catch either a Thameslink train or fast service to London, which you then have to give more time for travelling.