They need to decide what they intend to do development wise down that way.
Unless the intention is to allow development towards Hastings, with Frankston as a major CBD, the thing should just be closed. It is not economically feasible to electrify part of the line - it is all or nothing, as the further electrification reaches the less viable the diesel portion becomes.
However developing Frankston as a proper centre makes sense - the peninsula is already fairly self-contained, for residents of Frankston and Mornington Pen. respectively, workplaces are located:
Frankston >>> 33% / 11%
Mornington Pen >>> 9% / 55%
Dandenong >>> 11% / 5%
Casey >>> 5% / 3%
Kingston >>> 10% / 4%
City of Melb / Yarra / Port Phillip >>> 8% / 6%
An express rail connection from Frankston up to Dandenong (eg. via Eastlink and Eumemmerring Creek or Western Port Hwy) is justifiable, which would help support both Frankston and Dandenong as major suburban CBDs. In terms of Frankston specifically, provision of express services in this manner is beneficial as it eliminates the need for any track amplification south of Caulfield. The catchment of the Frankston line drops significantly past Mentone, hence it is not economical or indeed necessary to provide express service for the section between Caulfield and Frankston.
This also increases the benefits of quadding between Caulfield and Dandenong, and there's no reason travel time could not get down to 20min city to Dandenong (conservatively) giving:
*City to Dandenong Stopping - 42min
*City to Frankston Stopping - 64min
*City to Dandenong Express - 20min
>>>Dandenong - Frankston +15min
>>>Dandenong - Stony Point +50min
>>>Dandenong - Clyde +20min
>>>Dandenong - Pakenham +27min
>>>Dandenong - Traralgon +80-90min
That is, savings of around 25min and 30min to Dandenong and Frankston respectively. With Frankston as a self-sufficient CBD, one would push for development along the Stony Point line towards Hastings. The only justification for keeping the entire line beyond Hastings to Stony Point is if the ferry service to Phillip Island is developed as the primary public transport route. Given a half hour ferry trip, this is not an unreasonable proposition compared with the 2hr20min coach journey from Dandenong to Cowes.