Uckfield would mean they could stable a train there and late running trains wouldn’t have to be kept being turned around at Crowborough because there is already a train in the single line section
Southern have explored the option of berthing trains on the single line at Uckfield (and indeed have looked at berthing overnight at Crowborough in the event of stock getting stranded due to incidents further north). The problem with Uckfield in particular is that it’s a bloomin’ long taxi journey from any crew depot, but more to the point, the units would also not be in a secure enough environment overnight. The risk of vandalism at Uckfield is apparently deemed pretty high, which I can well understand given some of the “clientele” who can be seen on the platforms from mid-morning through to the small hours. If you were to berth trains, you’d also have to look at station security too.
As for Crowborough, terminating trains there is to avoid delayed northbound workings impacting on the timetable through Oxted / East Croydon, not really to do with the single line. They would be the very trains which would next occupy the single line anyway. Indeed, in many cases in the peaks, it actually ends up being better to send trains all the way through, otherwise there may be a unit sitting in the platform needing to head back the other way before the next train can make it through from Ashurst Jn (and besides that, passengers tend to now refuse to leave terminating trains, which causes even more problems).
The real reason you’d want to re-double the track and stations is to avoid the inevitable regulating issues which lead to a lot of the late running and suchlike, especially around Cowden. Cowden is such an enormous constraint that it seriously holds back even hourly service on the line, and if only one part were to be sensibly doubled, that would be it. The trackbed is still there and even some of the old platform (albeit needing a bit more than a revamp...).