3rd Rail to Overhead Line Conversion?

After the heavy snowfalls, arctic temperatures and widespread disruption caused on the southern region rail network in Britain last winter, there have been calls for the conversion of the 3rd rail power supply system to an overhead system that isn't so vulnerable to freezing weather.  So, why would we (the country, I mean) do this in a recession when money is tight and:

• we've just spent £130million upgrading the 3rd rail power system;
• it would cost about £2.5billion to convert it;
• it would cost about £200k to convert each 4-car unit using the system and there are hundreds of those;
• the conversion would transfer the weather problems from ice and snow to high winds;
• we only get, on average, a few days of ice disruption each year.

Thinking about it, why would we ever do it, regardless of a recession?