If TfL is still largely funded by the taxpayer, how does shifting control of the line save the Treasury from expenditure? It might be different columns but its still spending.
Because even with five additional footbridges, it is highly likely that 4th rail electrification will come out much cheaper than a 25kV installation, given the cost of the latter continues to rise into the stratosphere (£2.5m+/stkm?).
There will also be no need to electrify the section of the line south of Harrow on the Hill since it probably wouldn't really be used in such an arrangement which saves several track kilometres.
Given the downturn in peak traffic on the sub-surface lines post coronavirus, you probably could run it, at least partially, using slack in the existing S-stock fleet.
Also, capex is the spending the treasury prefers, because politicians get to make pithy statements about investing in infrastructure. Hence the dressing up of.engineering renewals as 'upgrades'. It's open the treasury doesn't want and as this section isn't going to cover its costs for LUL guess who's going to be giving TfL an allowance for the branch?
The same people who would pay for it to stay open if it stays as it is?
Closing the line is politically impossible, the question is what option costs the treasury least.
Electrification at 25kV will cost more than conversion to London Underground.