Lower cost rail electrification.

[adam2]

Electrified railways are in general a good thing as diesel oil use is thereby reduced.
Significant extension of of conductor rail schemes is de facto banned due to the risks.
Extensions of 25 KV AC are hugely expensive.

I therefore suggest an alternative for branch lines and lightly used rail routes, namely overhead electrification at 750 volts DC. This is already used for tramways, so the equipment is fairly standard.
Trains powered by 750 volts DC are a well understood system, widely used in the South East and on Merseyside, the train need not "know" that the supply is from an overhead wire rather than from a live rail.

Advantages include
Lower cost of the overhead line equipment, smaller insulators and reduced clearances. Equipment less visually obtrusive.
Cheaper to supply the traction current with less need for costly grid upgrades.

The main drawback is the reduced power available, if the current is to be limited to a reasonable figure. 25 KV AC would still be needed for high speed mainlines, or those routes handling long and heavy freight or passenger trains.
But for branch lines that are at present diesel powered it sounds worth pursuing.
Dual voltage trains could be used for through services, some already exist.

[BritDownUnder]

I don't want to rain on anyone's parade but would there not be a difference between the very large cross section rail and a relatively thin/small cross section overhead line? A smaller cross section conductor with lower voltage and higher current inevitably leads to a higher volt drop and less efficient use of the power but hardly a show stopper. I also think that the third rails are fed from some cable at regular intervals as iron is a much poorer conductor than copper or aluminium.

I do know that the Wellington NZ rail system uses 1500 VDC as its power source. Also uses a 1 metre gauge or something like that making for tighter curves etc. Not very long trains but a lot of steep inclines as Wellington is very hilly. I spent a miserable half year as a civil servant in Wellington travelling this line. Also drivers view of the same Johnsonville line.

[adam2]

The greater resistance of an overhead wire if compared to a conductor rail is a potential problem, but is not great as supposed. Remember that that the conductor wire will be copper, which has a much lower resistance than the steel used for conductor rails. Also the contact wire is suspended from a catenary wire and attached thereto by dropper wires of variable length so as to maintain an almost constant height above the rails. This catenary wire is electrically part of the same circuit as the contact wire, this reduces the resistance.
The contact wire gradually wears away and needs periodic replacement, the catenary wire lasts almost indefinitely.

Historically, UK tramways (including street running railways) were limited to 550 volts DC, but 750 volts is now permitted. For an electric railway on a dedicated and fenced right of way, higher voltages were allowed, such as 1,500 volts. 1,500 volts DC is used overseas but has not been used in the UK for decades. AFAIK the last 1,500 volt DC line in the uk was the Woodhead route, which closed over 40 years ago.
A higher voltage might be attractive, but is moving away from a cheap and simple scheme that uses readily available equipment. Limiting the voltage to 750 volts also allows extensions onto street running, and potential interoperability with street running trams.